sequence_id stringlengths 7 7 | sequence_name stringlengths 4 573 | sequence listlengths 1 348 | keywords listlengths 1 7 | score int64 1 2.47k | offset_a int64 -14,827 666,262,453B | offset_b int64 0 635M ⌀ | cross_references listlengths 1 128 ⌀ | former_ids listlengths 1 3 ⌀ | author stringlengths 7 231 ⌀ | timestamp timestamp[us]date 1999-12-11 03:00:00 2026-01-19 02:46:49 | filename stringlengths 29 29 | hash stringlengths 32 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A391543 | Expansion of e.g.f. exp(g^3 - 1), where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"3",
"27",
"357",
"6201",
"133083",
"3395619",
"100313181",
"3365491761",
"126353541843",
"5247146593899",
"238762376683317",
"11812298088897513",
"631226977556646123",
"36232167030479087859",
"2223141931879664490477",
"145203861075389109473121",
"10058197199128695920525859"
] | [
"nonn"
] | 16 | 0 | 2 | [
"A000108",
"A250916",
"A391543",
"A391544",
"A391554"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T05:37:22 | oeisdata/seq/A391/A391543.seq | b0ffbf870854d5842e60cf7f9bfad3a8 |
A391544 | Expansion of e.g.f. exp(g^4 - 1), where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"4",
"44",
"688",
"13864",
"340544",
"9841216",
"326498176",
"12214596032",
"508259328256",
"23269655140096",
"1161912882351104",
"62816589188575744",
"3654517810229321728",
"227597447625495486464",
"15105030195892500373504",
"1064087464840967635111936",
"792909189984017517521... | [
"nonn"
] | 15 | 0 | 2 | [
"A000108",
"A250916",
"A391543",
"A391544",
"A391555"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T07:11:16 | oeisdata/seq/A391/A391544.seq | b2c359344bfe8f3f949c6959bfd9d50b |
A391545 | Expansion of e.g.f. exp(g^2 - 1), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"2",
"18",
"272",
"5812",
"161112",
"5500744",
"223415936",
"10529259024",
"565135093664",
"34045145461024",
"2275337355049728",
"167102361753877312",
"13378718058724535168",
"1159904199850601405568",
"108268982677754935390208",
"10826634986211198785741056",
"11547701360033327... | [
"nonn"
] | 15 | 0 | 2 | [
"A001764",
"A391545",
"A391546",
"A391547",
"A391556"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T09:44:42 | oeisdata/seq/A391/A391545.seq | 0d9cd63806525030407b44a7864919c7 |
A391546 | Expansion of e.g.f. exp(g^3 - 1), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"3",
"33",
"573",
"13617",
"411183",
"15072489",
"650252529",
"32284539009",
"1813630146651",
"113752664510769",
"7880888252411397",
"597800960080948017",
"49282909533714860487",
"4388007245760196544313",
"419685340277699761142457",
"42916708159524954104566401",
"4672893727892... | [
"nonn"
] | 15 | 0 | 2 | [
"A001764",
"A391545",
"A391546",
"A391547",
"A391557"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T09:44:45 | oeisdata/seq/A391/A391546.seq | 933101549295594c0ba42e9a4dc92f1a |
A391547 | Expansion of e.g.f. exp(g^4 - 1), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"4",
"52",
"1024",
"26968",
"888544",
"35136256",
"1620888448",
"85448232256",
"5067327054592",
"333892475942656",
"24201538373054464",
"1913830001496212992",
"163975129736104044544",
"15132238166103973470208",
"1496471873412346550247424",
"157887765054017375739252736",
"17703... | [
"nonn"
] | 16 | 0 | 2 | [
"A001764",
"A380512",
"A391545",
"A391546",
"A391547",
"A391558"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T12:48:06 | oeisdata/seq/A391/A391547.seq | 92ce4a94c70672b8dc3c1c807497a9e4 |
A391548 | Expansion of e.g.f. exp(g^2 - 1), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"2",
"22",
"428",
"12076",
"448712",
"20738824",
"1148149424",
"74131413136",
"5471986811552",
"454711729662304",
"42019423659958208",
"4275130751389582528",
"474935384360600400512",
"57209906771265164558464",
"7427930782722522024965888",
"1034154561319373303869624576",
"15369... | [
"nonn"
] | 15 | 0 | 2 | [
"A002293",
"A380516",
"A391548",
"A391549",
"A391550",
"A391559"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T09:45:18 | oeisdata/seq/A391/A391548.seq | acea0599f72569add49281f984c20764 |
A391549 | Expansion of e.g.f. exp(g^3 - 1), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"3",
"39",
"843",
"25641",
"1008783",
"48784599",
"2802490407",
"186608164689",
"14139309157083",
"1201681426617639",
"113242150754693667",
"11721524664493786041",
"1322202193368792839847",
"161456204483717067230679",
"21221349737155871410108287",
"2987457553977680268696851361",... | [
"nonn"
] | 15 | 0 | 2 | [
"A002293",
"A380516",
"A391548",
"A391549",
"A391550",
"A391560"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-24T08:45:16 | oeisdata/seq/A391/A391549.seq | d95e18b8221658b52a0ade9ba4a4551f |
A391550 | Expansion of e.g.f. exp(g^4 - 1), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"4",
"60",
"1432",
"46984",
"1964544",
"99929056",
"5991976960",
"414015246528",
"32400442245376",
"2833433743081216",
"273895764519842304",
"29006040307478648320",
"3340227044053214851072",
"415614838629786639120384",
"55572930926734714107142144",
"7947546303663092651291938816"... | [
"nonn"
] | 14 | 0 | 2 | [
"A002293",
"A380516",
"A391548",
"A391549",
"A391550",
"A391561"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-23T15:28:01 | oeisdata/seq/A391/A391550.seq | 436a2c1ec049140baaf43dce53bcae7f |
A391552 | Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * (3+j)^n. | [
"1",
"3",
"1",
"9",
"7",
"2",
"27",
"37",
"24",
"6",
"81",
"175",
"194",
"108",
"24",
"243",
"781",
"1320",
"1230",
"600",
"120",
"729",
"3367",
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"11340",
"9120",
"3960",
"720",
"2187",
"14197",
"47544",
"92526",
"109200",
"77280",
"30240",
... | [
"nonn",
"tabl",
"easy"
] | 79 | 0 | 2 | [
"A007318",
"A028246",
"A038719",
"A048993",
"A131689",
"A391552",
"A391633",
"A391635"
] | null | Kolosov Petro, Dec 13 2025 | 2025-12-29T22:19:11 | oeisdata/seq/A391/A391552.seq | 7196d709585745a135002ea299a96bf9 |
A391553 | Expansion of e.g.f. exp((g^2 - 1)/2), where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"1",
"6",
"58",
"778",
"13386",
"281476",
"7000876",
"201163068",
"6559979068",
"239428935496",
"9672134739576",
"428510225570296",
"20661898792071928",
"1077289606360647408",
"60398988138132738256",
"3623792843060787912976",
"231683722216692321900816",
"15725444708263745576... | [
"nonn"
] | 13 | 0 | 3 | [
"A000108",
"A250916",
"A391553"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T14:42:11 | oeisdata/seq/A391/A391553.seq | 84be3f3aa3c6f32217103fbf17211f79 |
A391554 | Expansion of e.g.f. exp((g^3 - 1)/3), where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"1",
"7",
"75",
"1089",
"20001",
"444711",
"11614107",
"348509505",
"11816697249",
"446808836871",
"18641920151691",
"850777764125697",
"42162606476192385",
"2254918424892662439",
"129452195262941386011",
"7940526673653916461441",
"518303074153507655696577",
"358715727210370... | [
"nonn"
] | 14 | 0 | 3 | [
"A000108",
"A391543",
"A391554"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-22T04:10:14 | oeisdata/seq/A391/A391554.seq | de3f21cdf58dc0dbff57954c89a06bcf |
A391555 | Expansion of e.g.f. exp((g^4 - 1)/4), where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"1",
"8",
"94",
"1468",
"28676",
"673096",
"18456208",
"578989664",
"20451955168",
"803281220416",
"34725507491456",
"1638442250105728",
"83783085867535744",
"4615534061313644288",
"272513023397196560896",
"17167327855852316678656",
"1149361306938635404179968",
"814955639557... | [
"nonn"
] | 15 | 0 | 3 | [
"A000108",
"A391544",
"A391555"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-22T12:40:23 | oeisdata/seq/A391/A391555.seq | 152d7f491935bc5bf78daa68cf25aff4 |
A391556 | Expansion of e.g.f. exp((g^2 - 1)/2), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"1",
"8",
"112",
"2266",
"60266",
"1991416",
"78760648",
"3630762332",
"191265470236",
"11339034426496",
"747343586057696",
"54219279828815608",
"4294310822951749432",
"368738274887057206496",
"34122945513257911827616",
"3385693640030179229760016",
"358570966134764272331164688... | [
"nonn"
] | 13 | 0 | 3 | [
"A001764",
"A391545",
"A391556"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-22T10:06:37 | oeisdata/seq/A391/A391556.seq | 09b3db6b0661d506dab3a96a422e39e9 |
A391557 | Expansion of e.g.f. exp((g^3 - 1)/3), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"1",
"9",
"135",
"2865",
"78981",
"2684721",
"108655779",
"5106054465",
"273406908105",
"16438153575321",
"1096777967659551",
"80433633647877489",
"6431883559148239245",
"557038051659369897345",
"51947423242094451402171",
"5190379048351466059523841",
"5532066860393062669702654... | [
"nonn"
] | 13 | 0 | 3 | [
"A001764",
"A391546",
"A391557"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-22T04:10:11 | oeisdata/seq/A391/A391557.seq | 6350261d1b1677c18af4e24f517d7bbb |
A391558 | Expansion of e.g.f. exp((g^4 - 1)/4), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"1",
"10",
"160",
"3556",
"101596",
"3554896",
"147394360",
"7070846560",
"385443921376",
"23540859594496",
"1592702310316096",
"118266614013880960",
"9563910530472069760",
"836757720010749093376",
"78759942872852607506176",
"7936484353607159233624576",
"8525273717974120138675... | [
"nonn"
] | 13 | 0 | 3 | [
"A001764",
"A391547",
"A391558"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-21T14:42:15 | oeisdata/seq/A391/A391558.seq | ae645652cd0d92150f0db20d5e4cfcb2 |
A391559 | Expansion of e.g.f. exp((g^2 - 1)/2), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"10",
"184",
"5002",
"180946",
"8194876",
"446499040",
"28458981244",
"2078421338332",
"171172926117496",
"15697577655564256",
"1586608160726540920",
"175250235244856579224",
"21003839031922634413072",
"2714857174269749946558976",
"376464923925271242105926416",
"557501719... | [
"nonn"
] | 13 | 0 | 3 | [
"A002293",
"A391548",
"A391559"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-22T12:36:04 | oeisdata/seq/A391/A391559.seq | 63dd9ba098e65f56d5facdf2d23ed264 |
A391560 | Expansion of e.g.f. exp((g^3 - 1)/3), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"11",
"213",
"5985",
"221661",
"10218531",
"564561201",
"36390748353",
"2682479586105",
"222652398049371",
"20554978625001261",
"2089547699051558241",
"231964689103531639893",
"27924323112643836661875",
"3623564792426316196908681",
"504240479834595078024218241",
"74908344... | [
"nonn"
] | 12 | 0 | 3 | [
"A002293",
"A391549",
"A391560"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-23T15:27:55 | oeisdata/seq/A391/A391560.seq | b1e0e687138a6fe2142449aa82993bfe |
A391561 | Expansion of e.g.f. exp((g^4 - 1)/4), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"12",
"244",
"7084",
"268716",
"12618616",
"707542312",
"46164369504",
"3437762234464",
"287830529920576",
"26772093907478976",
"2739431829975444352",
"305869238654653788544",
"37010335831481152199424",
"4824682223713815167769856",
"674162053956687816905529856",
"10052660... | [
"nonn"
] | 12 | 0 | 3 | [
"A002293",
"A391550",
"A391561"
] | null | Seiichi Manyama, Dec 13 2025 | 2025-12-23T15:27:51 | oeisdata/seq/A391/A391561.seq | c1d38cbf6c5790d463b42397a474bf1c |
A391562 | Number of subsets of {1..n} where no two elements sum to a prime. | [
"1",
"2",
"3",
"5",
"7",
"12",
"17",
"26",
"38",
"56",
"74",
"112",
"150",
"229",
"328",
"479",
"630",
"937",
"1278",
"1895",
"2610",
"3797",
"4984",
"7312",
"9640",
"14200",
"19068",
"27936",
"36982",
"54918",
"72854",
"107920",
"144416",
"214079",
... | [
"nonn",
"new"
] | 32 | 0 | 2 | [
"A000040",
"A002808",
"A391562"
] | null | Siddharth Joshi, Jan 10 2026 | 2026-01-18T23:09:01 | oeisdata/seq/A391/A391562.seq | 8bea35871a4e45b7386c410e40ec77d1 |
A391564 | Numerator of the constant term of the remainder obtained when Stern polynomial B(n,x) is divided by B(5,x). | [
"1",
"-1",
"1",
"1",
"0",
"-1",
"3",
"-1",
"1",
"0",
"-1",
"1",
"1",
"-3",
"5",
"1",
"1",
"-1",
"1",
"0",
"-1",
"1",
"-1",
"-1",
"5",
"-1",
"1",
"3",
"1",
"-5",
"11",
"-1",
"3",
"-1",
"0",
"1",
"1",
"-1",
"1",
"0",
"-1",
"1",
"-1",
... | [
"sign",
"frac",
"look"
] | 16 | 1 | 7 | [
"A125184",
"A186891",
"A260443",
"A391564",
"A391565",
"A391566"
] | null | Antti Karttunen, Dec 14 2025 | 2025-12-14T19:32:51 | oeisdata/seq/A391/A391564.seq | ab6cb2c704dc6910a84efb28abdd7fc9 |
A391565 | Denominator of the constant term of the remainder obtained when Stern polynomial B(n,x) is divided by B(5,x). | [
"1",
"2",
"2",
"4",
"1",
"4",
"4",
"8",
"4",
"1",
"4",
"8",
"2",
"8",
"8",
"16",
"8",
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"1",
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"16",
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"32",
"16",
"16",
"1",
"16",
"8",
"8",
"4",
"1",
"4",
"8",
"8",
"16",
... | [
"nonn",
"frac"
] | 8 | 1 | 2 | [
"A125184",
"A186891",
"A260443",
"A391564",
"A391565"
] | null | Antti Karttunen, Dec 14 2025 | 2025-12-14T12:02:00 | oeisdata/seq/A391/A391565.seq | 24791f7e0a5433eb97cd06b16b904e23 |
A391566 | Numbers k such that Stern polynomial B(k,x) is a multiple of B(5,x). | [
"5",
"10",
"20",
"35",
"40",
"45",
"70",
"75",
"80",
"85",
"90",
"105",
"140",
"150",
"155",
"160",
"165",
"170",
"180",
"210",
"275",
"280",
"285",
"300",
"310",
"315",
"320",
"325",
"330",
"340",
"355",
"360",
"365",
"420",
"535",
"550",
"555... | [
"nonn"
] | 13 | 1 | 1 | [
"A125184",
"A186891",
"A260443",
"A389916",
"A391346",
"A391564",
"A391566"
] | null | Antti Karttunen, Dec 14 2025 | 2025-12-15T01:48:09 | oeisdata/seq/A391/A391566.seq | d24807832881b5a7ad4cdf1a9e75f2f0 |
A391567 | If n is a power of 2, then a(n) = 1, otherwise we search for the smallest integer m > n, for which there exists an odd number i <= n^3 such that m*i = A048720(n, i), and return that i as the result of a(n). Here A048720 is carryless base-2 multiplication. | [
"1",
"1",
"3",
"1",
"7",
"3",
"7",
"1",
"15",
"7",
"3",
"3",
"5",
"7",
"15",
"1",
"31",
"15",
"3",
"7",
"5",
"3",
"45",
"3",
"31",
"5",
"2295",
"7",
"31",
"15",
"31",
"1",
"63",
"31",
"3",
"15",
"45",
"3",
"5",
"7",
"7",
"5",
"5",
... | [
"nonn"
] | 20 | 1 | 3 | [
"A048720",
"A115857",
"A115873",
"A391567",
"A391568",
"A391570",
"A391572"
] | null | Antti Karttunen, Dec 15 2025 | 2025-12-16T11:54:35 | oeisdata/seq/A391/A391567.seq | 62418d0725f3796bd85ea4a389e82b1e |
A391568 | Numbers k for which there exists an integer m in range k+1 .. A065621(k)-1 and an odd number i <= k^3 such that m*i = A048720(k, i), where A048720 is carryless base-2 multiplication. | [
"19",
"21",
"23",
"27",
"35",
"37",
"38",
"39",
"41",
"42",
"43",
"45",
"46",
"47",
"51",
"54",
"55",
"59",
"67",
"69",
"70",
"71",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"81",
"82",
"83",
"84",
"85",
"86",
"87",
"89",
"90",
"91",
"92"... | [
"nonn",
"base"
] | 18 | 1 | 1 | [
"A048720",
"A065621",
"A115857",
"A115873",
"A391567",
"A391568"
] | null | Antti Karttunen, Dec 15 2025 | 2025-12-16T11:54:31 | oeisdata/seq/A391/A391568.seq | bdb584f051b13355f81c50529b801894 |
A391569 | a(n) = n XOR A391573(n). | [
"0",
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"0",
"0",
"12",
"0",
"8",
"8",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"24",
"4",
"0",
"0",
"16",
"20",
"16",
"16",
"0",
"20",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"0",
"0",
"48",
"48",
... | [
"nonn",
"base",
"look"
] | 12 | 1 | 7 | [
"A003987",
"A048720",
"A391569",
"A391573",
"A391578",
"A391579",
"A391586"
] | null | Antti Karttunen, Dec 19 2025 | 2025-12-19T13:50:25 | oeisdata/seq/A391/A391569.seq | 654930d71619e0bba3f73717128f9844 |
A391570 | a(n) is the smallest odd k > 1 such that k*n = A048720(k,m) for some m, where A048720 is carryless base-2 multiplication. | [
"3",
"3",
"3",
"3",
"3",
"3",
"7",
"3",
"3",
"3",
"3",
"3",
"3",
"7",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"7",
"3",
"3",
"3",
"5",
"7",
"31",
"3",
"31",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"5",
"3",
"3",
"3",
"3",
"3",
"3",
... | [
"nonn",
"base"
] | 27 | 1 | 1 | [
"A003714",
"A048720",
"A391567",
"A391570",
"A391571",
"A391572",
"A391573",
"A391574",
"A391575",
"A391582",
"A391725"
] | null | Antti Karttunen, Dec 15 2025 | 2025-12-19T12:40:31 | oeisdata/seq/A391/A391570.seq | 306424b6d309fea01097e0e1f1816a7b |
A391571 | a(n) is the value of A280500(n*k, k) for the smallest odd k > 1 for which this value is not zero, where A280500 implements the carryless base-2 division, and returns 0 if the division leaves nonzero remainder. | [
"1",
"2",
"7",
"4",
"5",
"14",
"11",
"8",
"9",
"10",
"31",
"28",
"29",
"22",
"27",
"16",
"17",
"18",
"23",
"20",
"21",
"62",
"59",
"56",
"57",
"58",
"43",
"44",
"37",
"54",
"35",
"32",
"33",
"34",
"39",
"36",
"37",
"46",
"63",
"40",
"41... | [
"nonn",
"base"
] | 30 | 1 | 2 | [
"A003714",
"A048720",
"A115857",
"A280500",
"A391570",
"A391571",
"A391572",
"A391573",
"A391580",
"A391581",
"A391583",
"A391726"
] | null | Antti Karttunen, Dec 15 2025 | 2025-12-19T12:40:46 | oeisdata/seq/A391/A391571.seq | a3e2069e7b81df1099c6c9c49f80c791 |
A391572 | a(n) is the smallest odd k > 1 which divides A048720(n,k) [in ordinary arithmetic], where A048720 is carryless base-2 multiplication. | [
"3",
"3",
"5",
"3",
"3",
"5",
"3",
"3",
"3",
"3",
"7",
"5",
"7",
"3",
"17",
"3",
"3",
"3",
"5",
"3",
"3",
"7",
"3",
"5",
"5",
"7",
"3",
"3",
"3",
"17",
"3",
"3",
"3",
"3",
"5",
"3",
"3",
"5",
"3",
"3",
"3",
"3",
"5",
"7",
"17",
... | [
"nonn",
"base"
] | 22 | 1 | 1 | [
"A003714",
"A048720",
"A391570",
"A391571",
"A391572",
"A391573",
"A391576",
"A391577",
"A391735"
] | null | Antti Karttunen, Dec 16 2025 | 2025-12-19T12:40:50 | oeisdata/seq/A391/A391572.seq | c54d731c7688d3d85066b0ec3616279d |
A391573 | a(n) is the value of quotient A048720(n,k)/k for the smallest odd k > 1 for which A048720(n,k) is a multiple of k (in ordinary arithmetic), where A048720 is carryless base-2 multiplication. | [
"1",
"2",
"3",
"4",
"5",
"6",
"3",
"8",
"9",
"10",
"7",
"12",
"5",
"6",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"14",
"19",
"24",
"25",
"10",
"15",
"12",
"13",
"30",
"11",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"35",
"40",
"41",
... | [
"nonn",
"base"
] | 25 | 1 | 2 | [
"A003714",
"A048720",
"A391569",
"A391570",
"A391571",
"A391572",
"A391573",
"A391578",
"A391579",
"A391736"
] | null | Antti Karttunen, Dec 16 2025 | 2025-12-19T12:40:53 | oeisdata/seq/A391/A391573.seq | eb9b0714a94129d1ca5443dcb5d8fd62 |
A391574 | Numbers k such that 3*k = A048720(3,m) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"13",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"24",
"25",
"26",
"30",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"40",
"41",
"42",
"43",
"44",
"45",
"47",
"48",
"49",
"50"... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A003714",
"A048720",
"A391570",
"A391574",
"A391575",
"A391576"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T21:34:07 | oeisdata/seq/A391/A391574.seq | 963f8d55363155367190fda87250decf |
A391575 | Numbers k such that 3*k = A048720(3,m) for some m > k, where A048720 is carryless base-2 multiplication. | [
"3",
"6",
"11",
"12",
"13",
"15",
"19",
"22",
"24",
"25",
"26",
"30",
"35",
"38",
"43",
"44",
"45",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"55",
"59",
"60",
"61",
"63",
"67",
"70",
"75",
"76",
"77",
"79",
"83",
"86",
"88",
"89",
"90",
... | [
"nonn",
"base"
] | 24 | 1 | 1 | [
"A003714",
"A004780",
"A007088",
"A022155",
"A048720",
"A048724",
"A280500",
"A391570",
"A391574",
"A391575",
"A391577"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-18T10:16:33 | oeisdata/seq/A391/A391575.seq | e7706ad259bc91a31469bce46b443492 |
A391576 | Numbers k such that A048720(3,k) = 3*m for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"2",
"4",
"5",
"7",
"8",
"9",
"10",
"14",
"16",
"17",
"18",
"20",
"21",
"23",
"27",
"28",
"29",
"31",
"32",
"33",
"34",
"36",
"37",
"39",
"40",
"41",
"42",
"46",
"54",
"56",
"57",
"58",
"62",
"64",
"65",
"66",
"68",
"69",
"71",
"72... | [
"nonn",
"base"
] | 9 | 1 | 2 | [
"A003714",
"A048720",
"A203463",
"A391572",
"A391574",
"A391576",
"A391577"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T21:34:14 | oeisdata/seq/A391/A391576.seq | 4911fa9d2b6c7ae715815ee02c46eb23 |
A391577 | Numbers k such that A048720(3,k) = 3*m for some m < k, where A048720 is carryless base-2 multiplication. | [
"7",
"14",
"23",
"27",
"28",
"29",
"31",
"39",
"46",
"54",
"56",
"57",
"58",
"62",
"71",
"78",
"87",
"91",
"92",
"93",
"95",
"99",
"107",
"108",
"109",
"111",
"112",
"113",
"114",
"116",
"117",
"119",
"123",
"124",
"125",
"127",
"135",
"142",... | [
"nonn",
"base"
] | 25 | 1 | 1 | [
"A003714",
"A004780",
"A007088",
"A036556",
"A048720",
"A048724",
"A391572",
"A391575",
"A391576",
"A391577"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-18T20:23:59 | oeisdata/seq/A391/A391577.seq | 2b149789c95a45e4b4cd208ec3e7ccfd |
A391578 | Numbers k for which A391573(k) < k. | [
"7",
"11",
"13",
"14",
"22",
"23",
"26",
"27",
"28",
"29",
"31",
"39",
"43",
"44",
"46",
"47",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"71",
"75",
"77",
"78",
"79",
"83",
"86",
"87",
"88",
"89",
"91",
"92",
"93",... | [
"nonn",
"base"
] | 6 | 1 | 1 | [
"A048720",
"A391573",
"A391578",
"A391579",
"A391580"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T21:34:26 | oeisdata/seq/A391/A391578.seq | da8dc82bd8f3172308c57973b56ca873 |
A391579 | Fixed points of A391573. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"12",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"24",
"25",
"30",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"40",
"41",
"42",
"45",
"48",
"49",
"50",
"51",
"60",
"64",
"65",
"66",
"67",
"68"... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A003714",
"A048720",
"A391573",
"A391578",
"A391579"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T21:34:23 | oeisdata/seq/A391/A391579.seq | 8d6543a2db787a5c0a1ec06532f0d2f8 |
A391580 | Numbers k for which A391571(k) > k. | [
"3",
"6",
"7",
"11",
"12",
"13",
"14",
"15",
"19",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"35",
"38",
"39",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
... | [
"nonn",
"base"
] | 12 | 1 | 1 | [
"A004780",
"A391571",
"A391580",
"A391581"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T17:16:53 | oeisdata/seq/A391/A391580.seq | d536de48cfada46ff671191b542d50f0 |
A391581 | Numbers k whose binary expansion contains 2 adjacent 1's and A391571(k) = k. | [
"1117",
"1351",
"1813",
"2234",
"2695",
"2702",
"3605",
"3626",
"4468",
"5383",
"5390",
"5404",
"5447",
"7189",
"7210",
"7252",
"7253",
"8733",
"8936",
"9309",
"9607",
"10759",
"10766",
"10780",
"10808",
"10894",
"14357",
"14378",
"14411",
"14420",
"14504"... | [
"nonn",
"base"
] | 8 | 1 | 1 | [
"A003714",
"A004780",
"A391571",
"A391580",
"A391581"
] | null | Antti Karttunen, Dec 17 2025 | 2025-12-17T17:17:52 | oeisdata/seq/A391/A391581.seq | dd3e9f82a15cfd0f4e7b181b359a9d19 |
A391582 | a(n) is the third odd number k such that k*n = A048720(k,m) for some m, where A048720 is carryless base-2 multiplication. | [
"5",
"5",
"5",
"5",
"7",
"5",
"9",
"5",
"5",
"7",
"15",
"5",
"5",
"9",
"5",
"5",
"5",
"5",
"5",
"7",
"5",
"15",
"31",
"5",
"5",
"5",
"7",
"9",
"33",
"5",
"33",
"5",
"5",
"5",
"5",
"5",
"7",
"5",
"7",
"7",
"7",
"5",
"5",
"15",
"5... | [
"nonn",
"base"
] | 14 | 1 | 1 | [
"A048720",
"A391570",
"A391582",
"A391583",
"A391725"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T20:23:23 | oeisdata/seq/A391/A391582.seq | 3095e3383c8ed64e5ce38f79e7b100c1 |
A391583 | a(n) is the value of A280500(n*k, k) for the third odd number k for which this value is not zero, where A280500 implements the carryless base-2 division, and returns 0 if the division leaves nonzero remainder. | [
"1",
"2",
"3",
"4",
"13",
"6",
"7",
"8",
"9",
"26",
"31",
"12",
"21",
"14",
"23",
"16",
"17",
"18",
"19",
"52",
"29",
"62",
"59",
"24",
"25",
"42",
"63",
"28",
"29",
"46",
"31",
"32",
"33",
"34",
"35",
"36",
"109",
"38",
"107",
"104",
"... | [
"nonn",
"base"
] | 12 | 1 | 2 | [
"A048720",
"A280500",
"A391571",
"A391582",
"A391583",
"A391726"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T20:23:26 | oeisdata/seq/A391/A391583.seq | d8043b66429da1fed11dc8aa1253800c |
A391584 | Odd numbers k such that 3*k = A048720(m,k) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"3",
"5",
"7",
"9",
"15",
"17",
"21",
"31",
"33",
"37",
"41",
"51",
"63",
"65",
"69",
"73",
"81",
"85",
"99",
"103",
"115",
"127",
"129",
"133",
"137",
"145",
"149",
"161",
"165",
"169",
"195",
"199",
"207",
"227",
"231",
"243",
"255",
... | [
"nonn",
"base"
] | 11 | 1 | 2 | [
"A048720",
"A391584",
"A391585",
"A391725"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-18T20:23:35 | oeisdata/seq/A391/A391584.seq | a3daa5bc2db372c4f1d0a79a3dcf5817 |
A391585 | Numbers k such that 3*k = A048720(m,k) for some m, where A048720 is carryless base-2 multiplication. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"17",
"18",
"20",
"21",
"24",
"28",
"30",
"31",
"32",
"33",
"34",
"36",
"37",
"40",
"41",
"42",
"48",
"51",
"56",
"60",
"62",
"63",
"64",
"65",
"66",
"68",
... | [
"nonn",
"base"
] | 18 | 1 | 3 | [
"A003714",
"A048717",
"A048720",
"A125121",
"A280500",
"A295235",
"A333762",
"A391584",
"A391585",
"A391740",
"A391742",
"A391744",
"A391846",
"A391848",
"A391850",
"A391852",
"A391854",
"A391856",
"A391858",
"A391860",
"A391925"
] | null | Antti Karttunen, Dec 18 2025 | 2025-12-23T15:03:10 | oeisdata/seq/A391/A391585.seq | 2dd00186714634a22f4814843cdff709 |
A391586 | a(n) = n XOR A391571(n). | [
"0",
"0",
"4",
"0",
"0",
"8",
"12",
"0",
"0",
"0",
"20",
"16",
"16",
"24",
"20",
"0",
"0",
"0",
"4",
"0",
"0",
"40",
"44",
"32",
"32",
"32",
"48",
"48",
"56",
"40",
"60",
"0",
"0",
"0",
"4",
"0",
"0",
"8",
"24",
"0",
"0",
"0",
"84",... | [
"nonn",
"base"
] | 7 | 1 | 3 | [
"A003714",
"A003987",
"A391569",
"A391571",
"A391580",
"A391581",
"A391586"
] | null | Antti Karttunen, Dec 19 2025 | 2025-12-19T20:10:32 | oeisdata/seq/A391/A391586.seq | ced83d9b7a8d171b3a8ddaa1b17f859e |
A391587 | a(n) = 2*n - A115873(n). | [
"1",
"3",
"3",
"7",
"3",
"9",
"7",
"15",
"3",
"13",
"19",
"21",
"21",
"21",
"15",
"31",
"3",
"21",
"31",
"33",
"11",
"41",
"39",
"45",
"19",
"47",
"23",
"49",
"27",
"45",
"31",
"63",
"3",
"37",
"55",
"57",
"67",
"69",
"71",
"73",
"19",
... | [
"nonn",
"base"
] | 8 | 1 | 2 | [
"A000051",
"A006068",
"A048720",
"A115873",
"A391587"
] | null | Antti Karttunen, Dec 19 2025 | 2025-12-19T22:44:25 | oeisdata/seq/A391/A391587.seq | 4860c06fea1785713dd5f6b9e372b658 |
A391588 | a(n) = A003817(n) XOR (A003817(n)*n). | [
"0",
"5",
"10",
"27",
"36",
"45",
"54",
"119",
"136",
"153",
"170",
"187",
"204",
"221",
"238",
"495",
"528",
"561",
"594",
"627",
"660",
"693",
"726",
"759",
"792",
"825",
"858",
"891",
"924",
"957",
"990",
"2015",
"2080",
"2145",
"2210",
"2275"... | [
"nonn",
"base"
] | 21 | 1 | 2 | [
"A000079",
"A003817",
"A003987",
"A020330",
"A048720",
"A048724",
"A087737",
"A115873",
"A391588",
"A391589"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-20T17:25:35 | oeisdata/seq/A391/A391588.seq | 43731a2927f510bf3db6d0affefb9793 |
A391589 | a(n) = A003817(n) - A115873(n), where A115873(n) = the least k >= 1 for which A048720(A065621(n),k) = n*k. | [
"0",
"2",
"0",
"6",
"0",
"4",
"0",
"14",
"0",
"8",
"12",
"12",
"10",
"8",
"0",
"30",
"0",
"16",
"24",
"24",
"0",
"28",
"24",
"28",
"0",
"26",
"0",
"24",
"0",
"16",
"0",
"62",
"0",
"32",
"48",
"48",
"56",
"56",
"56",
"56",
"0",
"32",
... | [
"nonn",
"base"
] | 9 | 1 | 2 | [
"A003817",
"A115873",
"A391587",
"A391588",
"A391589",
"A391590"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-20T17:25:50 | oeisdata/seq/A391/A391589.seq | aad3a6a25ecfaa7094ad13af5364bffd |
A391590 | Numbers k for which A115873(k) = A003817(k). | [
"1",
"3",
"5",
"7",
"9",
"15",
"17",
"21",
"25",
"27",
"29",
"31",
"33",
"41",
"45",
"51",
"53",
"59",
"63",
"65",
"73",
"85",
"89",
"93",
"97",
"99",
"101",
"105",
"107",
"109",
"113",
"115",
"117",
"119",
"121",
"125",
"127",
"129",
"145"... | [
"nonn",
"base"
] | 9 | 1 | 2 | [
"A003817",
"A048720",
"A115873",
"A391589",
"A391590",
"A391729"
] | null | Antti Karttunen, Dec 20 2025 | 2025-12-20T17:25:56 | oeisdata/seq/A391/A391590.seq | 6794accb928796f4478f50dcfebd1b0e |
A391592 | Maximum size of a subset S of {1..n} such that all subset sums of {1/k : k in S} are distinct. | [
"1",
"2",
"3",
"4",
"5",
"5",
"6",
"7",
"8",
"9",
"10",
"10",
"11",
"12",
"12",
"13",
"14",
"14",
"15",
"15",
"15",
"16",
"17",
"17",
"18",
"19",
"20",
"20",
"21",
"21",
"22",
"23",
"23",
"24",
"24",
"25",
"26",
"27",
"28",
"28",
"29",
... | [
"nonn",
"more",
"new"
] | 27 | 1 | 2 | [
"A384927",
"A391592"
] | null | Cong Lu, Jan 10 2026 | 2026-01-18T23:10:13 | oeisdata/seq/A391/A391592.seq | 2ea2ee06ac6b76ab77f664dc46d3306a |
A391594 | a(n) = Sum_{k=0..2*n} binomial(2*k,2*n-k). | [
"1",
"3",
"13",
"60",
"277",
"1278",
"5896",
"27201",
"125491",
"578949",
"2670964",
"12322413",
"56849086",
"262271568",
"1209982081",
"5582216355",
"25753389181",
"118812495276",
"548137914373",
"2528817970494",
"11666626519000",
"53823634568385",
"248313737774419",
"... | [
"nonn",
"easy",
"new"
] | 27 | 0 | 2 | [
"A000930",
"A108479",
"A376729",
"A376730",
"A376731",
"A391594",
"A392428",
"A392429",
"A392430"
] | null | Seiichi Manyama, Jan 11 2026 | 2026-01-11T10:26:27 | oeisdata/seq/A391/A391594.seq | fc9323551821b73f7cb5da4bed5812a5 |
A391595 | Number of compositions of n such that one maximal run is the longest. | [
"1",
"1",
"2",
"2",
"5",
"10",
"16",
"39",
"81",
"156",
"323",
"672",
"1334",
"2704",
"5471",
"10956",
"21985",
"44143",
"88366",
"176961",
"354236",
"708688",
"1417905",
"2836907",
"5675282",
"11354249",
"22717973",
"45457421",
"90965933",
"182051395",
"3... | [
"nonn"
] | 8 | 0 | 3 | [
"A011782",
"A387637",
"A389509",
"A389511",
"A389512",
"A391595"
] | null | John Tyler Rascoe, Dec 13 2025 | 2025-12-19T18:44:48 | oeisdata/seq/A391/A391595.seq | 41b6058ba72a35cc4a2aa135021e8aa5 |
A391596 | Numbers k such that (27^k - 4^k)/23 is prime. | [
"2",
"3",
"7",
"61",
"617",
"10427",
"21529"
] | [
"nonn",
"hard",
"more"
] | 5 | 1 | 1 | [
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A229542",
"A375161",
"A375236",
"A377031",
"A391596"
] | null | Robert Price, Dec 13 2025 | 2025-12-13T19:31:56 | oeisdata/seq/A391/A391596.seq | cbd71eaaf6fa810adeab397bd48bb9e2 |
A391598 | Primes that are perimeter^2 + hypotenuse^2 of a Pythagorean triple. | [
"1069",
"1889",
"3761",
"5741",
"9781",
"27941",
"58601",
"79481",
"114661",
"118369",
"127669",
"182029",
"229589",
"286061",
"374929",
"573481",
"590489",
"602821",
"704761",
"717149",
"753569",
"847109",
"949129",
"1013681",
"1131181",
"1233301",
"1287961",
"... | [
"nonn",
"new"
] | 19 | 1 | 1 | [
"A103606",
"A389589",
"A391598"
] | null | Will Gosnell and Robert Israel, Jan 12 2026 | 2026-01-14T17:25:21 | oeisdata/seq/A391/A391598.seq | c81197190c647b250f2e117fa6935846 |
A391599 | Minimum size of an intersecting family of n-sets such that every set of size at most n-1 is disjoint from at least one member of the family. | [
"1",
"3",
"6",
"9",
"13"
] | [
"nonn",
"hard",
"more",
"new"
] | 21 | 1 | 2 | [
"A051185",
"A391599"
] | null | Iddo Drori, Jan 12 2026 | 2026-01-18T17:50:50 | oeisdata/seq/A391/A391599.seq | 4bfa81b2e11230a79047b0bf752aa3bc |
A391600 | a(n) = Sum_{k=0..floor((2*n+1)/3)} binomial(2*k+1,2*n-3*k+1). | [
"1",
"1",
"3",
"5",
"11",
"22",
"44",
"92",
"181",
"379",
"750",
"1557",
"3109",
"6401",
"12872",
"26349",
"53228",
"108575",
"219918",
"447702",
"908140",
"1846804",
"3749001",
"7619870",
"15474230",
"31443013",
"63865592",
"129755543",
"263576791",
"535475... | [
"nonn",
"easy",
"new"
] | 15 | 0 | 3 | [
"A376726",
"A376727",
"A376728",
"A391600",
"A392454",
"A392487",
"A392488"
] | null | Seiichi Manyama, Jan 14 2026 | 2026-01-15T15:07:14 | oeisdata/seq/A391/A391600.seq | 4aee5a8489f3f935fb4382b80632a2a1 |
A391602 | a(n) is the largest number m such that A391449(m) = n. | [
"633555",
"80061344",
"1109496723125"
] | [
"nonn",
"hard",
"bref",
"more"
] | 40 | 0 | 1 | [
"A002378",
"A055932",
"A059957",
"A141399",
"A252489",
"A391449",
"A391602",
"A391885",
"A391970"
] | null | Ken Clements, Dec 13 2025 | 2026-01-04T17:16:36 | oeisdata/seq/A391/A391602.seq | 7633f40d8f9e929c915b2336409e2284 |
A391604 | Expansion of (g/(1 + x*g))^2, where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"0",
"6",
"30",
"209",
"1494",
"11199",
"86606",
"686208",
"5541870",
"45453140",
"377576166",
"3170203255",
"26860801348",
"229377866631",
"1972162956192",
"17058138862427",
"148326624473418",
"1295850784585071",
"11369144565997354",
"100128360768256440",
"88488710721... | [
"nonn"
] | 14 | 0 | 3 | [
"A002293",
"A387982",
"A391275",
"A391604"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-18T17:33:40 | oeisdata/seq/A391/A391604.seq | 89c353b7ef49b1da02d932dbd09f387a |
A391605 | Expansion of g^3/(1 + x*g), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"2",
"12",
"73",
"497",
"3587",
"27001",
"209591",
"1665646",
"13485312",
"110833730",
"922316562",
"7755716261",
"65800033320",
"562548456031",
"4841654246934",
"41915639949437",
"364767096232883",
"3189101901648337",
"27998052592334464",
"246727558875994408",
"218165... | [
"nonn"
] | 15 | 0 | 2 | [
"A002293",
"A387982",
"A390810",
"A391378",
"A391605",
"A391606",
"A391607"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-18T13:44:22 | oeisdata/seq/A391/A391605.seq | 267c1dc93884f8994ea3879f77d9ebe7 |
A391606 | Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"10",
"58",
"403",
"2924",
"22113",
"172213",
"1372044",
"11130261",
"91624156",
"763466227",
"6427041731",
"54578677149",
"466990198097",
"4022044368331",
"34841523036049",
"303370789888274",
"2653614010505109",
"23307012085832216",
"205469444942615266",
"1817484... | [
"nonn"
] | 14 | 0 | 3 | [
"A002293",
"A391277",
"A391606"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-19T08:37:37 | oeisdata/seq/A391/A391606.seq | 99c47da51ca1c6271ece9f04c68e7c3d |
A391607 | Expansion of (g/(1 + x*g))^3, where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"0",
"9",
"45",
"327",
"2376",
"18063",
"141132",
"1127310",
"9163422",
"75556587",
"630432066",
"5313144241",
"45162954870",
"386747902206",
"3333351936423",
"28893977255499",
"251726064142716",
"2202976652879265",
"19357712995962519",
"170722541662823184",
"151068517... | [
"nonn"
] | 14 | 0 | 3 | [
"A002293",
"A387982",
"A391278",
"A391607"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-18T10:46:24 | oeisdata/seq/A391/A391607.seq | c5496ff7fa599032b6d631705a572383 |
A391608 | Expansion of (g/(1 + x*g^2))^2, where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"0",
"4",
"22",
"150",
"1076",
"8063",
"62358",
"494081",
"3990220",
"32726676",
"271856860",
"2282553289",
"19339768464",
"165151550460",
"1419950097538",
"12281779992486",
"106794370882600",
"933005023771187",
"8185715349553440",
"72091808178774269",
"637113372643101... | [
"nonn"
] | 13 | 0 | 3 | [
"A002293",
"A390740",
"A391199",
"A391608"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-18T07:55:07 | oeisdata/seq/A391/A391608.seq | f7227bf2dc04c76952340487dd088f8d |
A391609 | Expansion of (g/(1 + x*g^2))^3, where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"0",
"6",
"33",
"231",
"1680",
"12722",
"99174",
"790695",
"6417782",
"52854210",
"440569659",
"3709925170",
"31512765744",
"269690266146",
"2323196695551",
"20128333751349",
"175286209221924",
"1533444732404226",
"13469998501882377",
"118760989817062512",
"10506027741... | [
"nonn"
] | 13 | 0 | 3 | [
"A002293",
"A390740",
"A391202",
"A391609"
] | null | Seiichi Manyama, Dec 14 2025 | 2025-12-18T01:22:07 | oeisdata/seq/A391/A391609.seq | 097b3a5cad3b81654face98c5ca65317 |
A391610 | Triangle T(n,k) read by rows: T(n,k) is the coefficient of x^k of the monic polynomial (1+x)^n + ((2*(1+x))^n - (2+x)^n) / x. | [
"1",
"2",
"1",
"5",
"5",
"1",
"13",
"21",
"10",
"1",
"33",
"76",
"62",
"19",
"1",
"81",
"245",
"290",
"160",
"36",
"1",
"193",
"726",
"1135",
"920",
"387",
"69",
"1",
"449",
"2023",
"3941",
"4235",
"2639",
"903",
"134",
"1",
"1025",
"5384",
... | [
"nonn",
"tabl"
] | 21 | 0 | 2 | [
"A005183",
"A008949",
"A052944",
"A083324",
"A388426",
"A391610"
] | null | F. Chapoton, Dec 14 2025 | 2025-12-20T20:17:04 | oeisdata/seq/A391/A391610.seq | baa88243bbd658e8cacc453f5d2ad65a |
A391612 | Number of ways of n-coloring the square grid graph G_(6,6) such that no rectangle exists with sides parallel to the axes having all 4 corners of the same color. | [
"0",
"0",
"0",
"70369113985920",
"203716633441803914880",
"2852707805646422930409600",
"3954411769340602937111483520",
"1437168447338696434494958613760",
"214257345124014051308838018927360",
"16785094841352261197117578211362560",
"805649135498177598934800941315347200"
] | [
"nonn",
"easy"
] | 13 | 0 | 4 | [
"A200045",
"A252778",
"A252779",
"A252780",
"A252839",
"A391612"
] | null | Jason Davies, Dec 14 2025 | 2025-12-21T16:02:55 | oeisdata/seq/A391/A391612.seq | 153f8de69bf62c16f390cd654506c78b |
A391616 | a(n) = a(n-1) + prime(a(n-1)) + 1 for n > 1, with a(1) = 1. | [
"1",
"4",
"12",
"50",
"280",
"2092",
"20346",
"249306",
"3736496",
"66865856",
"1401245768",
"33847580050",
"930148157934",
"28761310191816",
"991367334867536",
"37786551261953348",
"1581554815614071152"
] | [
"nonn",
"more"
] | 46 | 1 | 2 | [
"A000040",
"A074271",
"A391401",
"A391616"
] | null | Kaloian Ivanov, Dec 14 2025 | 2025-12-28T19:38:49 | oeisdata/seq/A391/A391616.seq | 73d1280eeab33844cac6bd334b72fae9 |
A391620 | Number of integer partitions of n > 0 that are not the first sums of any composition with all parts > 1. | [
"1",
"2",
"3",
"4",
"6",
"10",
"14",
"20",
"28",
"39",
"53",
"72",
"96",
"128",
"168",
"220",
"285",
"369",
"472",
"603",
"765",
"968",
"1216",
"1525",
"1901",
"2366",
"2929",
"3618",
"4450",
"5464",
"6681",
"8154",
"9918",
"12041",
"14572",
"176... | [
"nonn",
"new"
] | 12 | 1 | 2 | [
"A000041",
"A000726",
"A004709",
"A007775",
"A008484",
"A008965",
"A011782",
"A026797",
"A046099",
"A070211",
"A080671",
"A185325",
"A295341",
"A342527",
"A357213",
"A390307",
"A390362",
"A390446",
"A390447",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A39... | null | Gus Wiseman, Dec 30 2025 | 2026-01-04T23:27:44 | oeisdata/seq/A391/A391620.seq | 06b00dbea38555e59c3b6e2405862a27 |
A391621 | Number of nonnegative integer sequences whose first sums are the k-th composition in standard order. | [
"2",
"3",
"2",
"4",
"2",
"2",
"2",
"5",
"2",
"3",
"2",
"2",
"1",
"2",
"2",
"6",
"2",
"3",
"2",
"3",
"2",
"2",
"2",
"2",
"0",
"2",
"1",
"2",
"1",
"2",
"2",
"7",
"2",
"3",
"2",
"4",
"2",
"2",
"2",
"3",
"1",
"3",
"2",
"2",
"1",
"... | [
"nonn",
"new"
] | 10 | 1 | 1 | [
"A000120",
"A001511",
"A011782",
"A029837",
"A029931",
"A055396",
"A066099",
"A070939",
"A342527",
"A357213",
"A390432",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391621",
"A391622",
"A39... | null | Gus Wiseman, Dec 19 2025 | 2026-01-04T23:27:50 | oeisdata/seq/A391/A391621.seq | e49e2352ce039ba627d859bb88a4aaae |
A391622 | Numbers k such that there is a unique nonnegative sequence whose first sums are the k-th composition in standard order. | [
"13",
"27",
"29",
"41",
"45",
"50",
"54",
"55",
"59",
"61",
"77",
"83",
"91",
"93",
"101",
"105",
"108",
"110",
"111",
"114",
"118",
"119",
"123",
"125",
"141",
"145",
"155",
"157",
"162",
"166",
"167",
"169",
"173",
"178",
"182",
"183",
"187",... | [
"nonn",
"changed"
] | 18 | 1 | 1 | [
"A000120",
"A001511",
"A008965",
"A011782",
"A029837",
"A029931",
"A066099",
"A070939",
"A342527",
"A357213",
"A390307",
"A390362",
"A390432",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A39... | null | Gus Wiseman, Dec 19 2025 | 2026-01-05T16:55:40 | oeisdata/seq/A391/A391622.seq | 11b9d5a57b7a55bfb3841ae4f2e92f55 |
A391623 | Positive integers k such that there is more than one nonnegative sequence whose first sums are the k-th composition in standard order. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"26",
"28",
"30",
"31",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"42",
"43",
"44",
"46",
"47",... | [
"nonn",
"new"
] | 8 | 1 | 2 | [
"A000120",
"A001511",
"A011782",
"A029837",
"A029931",
"A066099",
"A070939",
"A342527",
"A357213",
"A390307",
"A390362",
"A390432",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A39... | null | Gus Wiseman, Jan 02 2026 | 2026-01-05T16:55:02 | oeisdata/seq/A391/A391623.seq | 3a0fdbcecf285a5403b42940c294a55e |
A391624 | Positive integers k such that there is at most one nonnegative sequence whose first sums are the k-th composition in standard order. | [
"13",
"25",
"27",
"29",
"41",
"45",
"49",
"50",
"51",
"54",
"55",
"57",
"59",
"61",
"77",
"81",
"83",
"89",
"91",
"93",
"97",
"98",
"99",
"101",
"102",
"103",
"105",
"108",
"109",
"110",
"111",
"113",
"114",
"115",
"118",
"119",
"121",
"123",... | [
"nonn",
"new"
] | 9 | 1 | 1 | [
"A000120",
"A005674",
"A011782",
"A029837",
"A029931",
"A066099",
"A070939",
"A357213",
"A390432",
"A390448",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391234",
"A391621",
"A391622",
"A391623",
"A391624",
"A39... | null | Gus Wiseman, Jan 03 2026 | 2026-01-05T16:55:35 | oeisdata/seq/A391/A391624.seq | 976557f89f8cc661e83c9e27703e1f58 |
A391626 | Numbers k such that the k-th composition in standard order is the first sums of some composition into parts > 1. | [
"8",
"16",
"32",
"64",
"128",
"136",
"256",
"264",
"272",
"512",
"520",
"528",
"544",
"1024",
"1032",
"1040",
"1056",
"1088",
"2048",
"2056",
"2064",
"2080",
"2112",
"2176",
"2184",
"4096",
"4104",
"4112",
"4128",
"4160",
"4224",
"4232",
"4352",
"436... | [
"nonn",
"new"
] | 5 | 1 | 1 | [
"A000120",
"A011782",
"A029931",
"A066099",
"A070211",
"A070939",
"A342527",
"A357213",
"A390307",
"A390432",
"A390446",
"A390448",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391235",
"A391620",
"A39... | null | Gus Wiseman, Jan 07 2026 | 2026-01-08T21:50:30 | oeisdata/seq/A391/A391626.seq | 8ba929f87e8d582799b4e807d9ff56a3 |
A391627 | Numbers k such that there is more than one composition whose first sums are the k-th composition in standard order. | [
"4",
"8",
"16",
"32",
"36",
"64",
"68",
"72",
"128",
"132",
"136",
"144",
"256",
"260",
"264",
"272",
"288",
"292",
"512",
"516",
"520",
"528",
"544",
"548",
"576",
"584",
"1024",
"1028",
"1032",
"1040",
"1056",
"1060",
"1088",
"1092",
"1096",
"1... | [
"nonn",
"new"
] | 5 | 1 | 1 | [
"A000079",
"A000120",
"A001511",
"A008965",
"A011782",
"A029837",
"A029931",
"A066099",
"A070211",
"A070939",
"A342527",
"A357135",
"A357213",
"A390307",
"A390362",
"A390432",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A39... | null | Gus Wiseman, Jan 07 2026 | 2026-01-08T21:50:25 | oeisdata/seq/A391/A391627.seq | 7b71c4dab84a6b27afcc5af04bcdf524 |
A391628 | Number of integer compositions of n that are the first sums of more than one composition. | [
"0",
"0",
"1",
"1",
"1",
"2",
"3",
"4",
"6",
"8",
"12",
"16",
"23",
"31",
"44",
"59",
"83",
"111",
"155",
"207",
"287",
"383",
"528",
"704",
"966",
"1287",
"1759",
"2342",
"3190",
"4245",
"5765",
"7668",
"10387",
"13810",
"18665",
"24807",
"334... | [
"nonn",
"easy",
"new"
] | 20 | 1 | 6 | [
"A008965",
"A011782",
"A022340",
"A066099",
"A070211",
"A342527",
"A357213",
"A390432",
"A390446",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A391235",
"A391621",
"A391623",
"A391627",
"A391628",
"A391642",
"A391644",
"A39... | null | Gus Wiseman, Jan 07 2026 | 2026-01-12T04:32:53 | oeisdata/seq/A391/A391628.seq | 9194970c4795894a0013953c157768bb |
A391629 | Number of multisets summing to n (or reversed partitions of n) that are not the first sums of any integer partition. | [
"1",
"1",
"2",
"3",
"6",
"9",
"14",
"19",
"29",
"40",
"55",
"73",
"100",
"133",
"175",
"227",
"296",
"382",
"489",
"623",
"791",
"1000",
"1254",
"1569",
"1957",
"2434",
"3009",
"3714",
"4564",
"5600"
] | [
"nonn",
"more",
"new"
] | 14 | 1 | 3 | [
"A000009",
"A000041",
"A000065",
"A008484",
"A046099",
"A111133",
"A295341",
"A325325",
"A368684",
"A389811",
"A390307",
"A390362",
"A390429",
"A390431",
"A390445",
"A390446",
"A390447",
"A390448",
"A390449",
"A390568",
"A390676",
"A390677",
"A390678",
"A391620",
"A39... | null | Gus Wiseman, Dec 31 2025 | 2026-01-04T23:27:24 | oeisdata/seq/A391/A391629.seq | e8f7b640d0747ab18e9f87f4982df1dc |
A391630 | Number of mutual-visibility sets in the n X n queen graph. | [
"2",
"16",
"495",
"59944",
"24935002"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 14 2025 | 2025-12-14T19:32:32 | oeisdata/seq/A391/A391630.seq | e0d350830a7d8e3da894c10fad83dab2 |
A391631 | Number of mutual-visibility sets in the n X n rook complement graph. | [
"2",
"7",
"334",
"58875",
"33405756"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 14 2025 | 2025-12-14T19:32:28 | oeisdata/seq/A391/A391631.seq | d6fdb1b67429f3d387e1c1d9cf00f5ed |
A391632 | Number of mutual-visibility sets in the n-Andrásfai graph. | [
"4",
"21",
"127",
"749",
"4455",
"26725",
"161007",
"971613",
"5866487",
"35426517",
"213940607",
"1291991757"
] | [
"nonn",
"more",
"changed"
] | 13 | 1 | 1 | null | null | Eric W. Weisstein, Dec 14 2025 | 2026-01-12T08:48:46 | oeisdata/seq/A391/A391632.seq | 0f04a2adf6d49c988f9ffef8ddcd5f4d |
A391633 | Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * (4+j)^n. | [
"1",
"4",
"1",
"16",
"9",
"2",
"64",
"61",
"30",
"6",
"256",
"369",
"302",
"132",
"24",
"1024",
"2101",
"2550",
"1830",
"720",
"120",
"4096",
"11529",
"19502",
"20460",
"13080",
"4680",
"720",
"16384",
"61741",
"140070",
"201726",
"186480",
"107520",... | [
"nonn",
"tabl",
"easy"
] | 51 | 0 | 2 | [
"A007318",
"A028246",
"A038719",
"A048993",
"A131689",
"A391552",
"A391633",
"A391635"
] | null | Kolosov Petro, Dec 14 2025 | 2025-12-29T10:12:25 | oeisdata/seq/A391/A391633.seq | 3a858822b0b4dd62dfc71888f79d4974 |
A391634 | Number of n X n binary matrices that contain no 3 X 3 zero submatrix. | [
"1",
"2",
"16",
"511",
"63935",
"29898526",
"49116829858",
"266752545057881"
] | [
"nonn",
"more"
] | 13 | 0 | 2 | [
"A001198",
"A175563",
"A350304",
"A391634"
] | null | Eric W. Weisstein, Dec 14 2025 | 2025-12-15T16:53:25 | oeisdata/seq/A391/A391634.seq | 1a5ecd9bec2026fc10d37d587b46df93 |
A391635 | Triangle read by rows: T(n,k) = Sum_{j=0..k} (-1)^(k-j) * binomial(k,j) * (5+j)^n. | [
"1",
"5",
"1",
"25",
"11",
"2",
"125",
"91",
"36",
"6",
"625",
"671",
"434",
"156",
"24",
"3125",
"4651",
"4380",
"2550",
"840",
"120",
"15625",
"31031",
"39962",
"33540",
"17760",
"5400",
"720",
"78125",
"201811",
"341796",
"388206",
"294000",
"1428... | [
"nonn",
"tabl",
"easy"
] | 49 | 0 | 2 | [
"A007318",
"A028246",
"A038719",
"A048993",
"A131689",
"A391552",
"A391633",
"A391635"
] | null | Kolosov Petro, Dec 14 2025 | 2025-12-29T10:12:38 | oeisdata/seq/A391/A391635.seq | 363f02a739840d6df9001d1dd1b2a12a |
A391641 | Number of integer compositions of n that are not the first sums of any composition with no 1's. | [
"1",
"2",
"4",
"7",
"15",
"31",
"63",
"126",
"253",
"508",
"1019",
"2041",
"4087",
"8179",
"16368",
"32745",
"65508",
"131032",
"262095",
"524219",
"1048491",
"2097034",
"4194158",
"8388407",
"16776967",
"33554091",
"67108442",
"134217152",
"268434744",
"536... | [
"nonn",
"easy",
"new"
] | 19 | 1 | 2 | [
"A000041",
"A008965",
"A011782",
"A070211",
"A080671",
"A342527",
"A357213",
"A390432",
"A390445",
"A390446",
"A390447",
"A390448",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391235",
"A391620",
"A391626",
"A39... | null | Gus Wiseman, Jan 01 2026 | 2026-01-15T20:37:22 | oeisdata/seq/A391/A391641.seq | de9a9bf22ca11406ccf81fe8cbfac57c |
A391642 | Number of integer compositions whose first sums are the n-th composition in standard order. | [
"0",
"1",
"0",
"2",
"0",
"0",
"0",
"3",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"5",
"0",
"1",
"0",
"2",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"... | [
"nonn"
] | 7 | 1 | 4 | [
"A000079",
"A000120",
"A011782",
"A029837",
"A029931",
"A066099",
"A070211",
"A070939",
"A342527",
"A357135",
"A357213",
"A390432",
"A390448",
"A390449",
"A390567",
"A390568",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390745",
"A390747",
"A391621",
"A39... | null | Gus Wiseman, Dec 25 2025 | 2025-12-29T09:34:03 | oeisdata/seq/A391/A391642.seq | 407386f8611d5bc349b44155bf01d896 |
A391643 | Number of integer compositions n that are the first sums of a unique nonnegative sequence. | [
"0",
"0",
"0",
"1",
"2",
"7",
"14",
"35",
"68",
"149",
"282",
"577",
"1070",
"2101",
"3836",
"7331",
"13226",
"24803",
"44334",
"82003",
"145508",
"266365",
"469898",
"853337",
"1498334",
"2703917",
"4729596",
"8492299",
"14808026",
"26480779",
"46055390",... | [
"nonn",
"easy",
"new"
] | 16 | 1 | 5 | [
"A000120",
"A008965",
"A011782",
"A070211",
"A342527",
"A357213",
"A390307",
"A390432",
"A390448",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391234",
"A391235",
"A391621",
"A391622",
"A391623",
"A391627",
"A39... | null | Gus Wiseman, Jan 04 2026 | 2026-01-12T04:33:36 | oeisdata/seq/A391/A391643.seq | 808e84f493fcf9ce03bee0e7964a6a2e |
A391644 | Number of integer compositions of n that are the first sums of a unique composition. | [
"0",
"1",
"0",
"1",
"2",
"3",
"4",
"8",
"10",
"19",
"24",
"43",
"56",
"96",
"126",
"211",
"278",
"457",
"604",
"978",
"1296",
"2073",
"2752",
"4359",
"5794",
"9104",
"12112",
"18905",
"25168",
"39065",
"52032",
"80384",
"107104",
"164807",
"219646"... | [
"nonn",
"easy",
"new"
] | 15 | 1 | 5 | [
"A008965",
"A011782",
"A022340",
"A066099",
"A070211",
"A342527",
"A357213",
"A390432",
"A390446",
"A390567",
"A390673",
"A390674",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A391234",
"A391235",
"A391621",
"A391622",
"A391627",
"A391628",
"A391641",
"A39... | null | Gus Wiseman, Jan 06 2026 | 2026-01-12T04:34:37 | oeisdata/seq/A391/A391644.seq | 7a039d19c3e7c0ceef468ca3fa8d31be |
A391645 | Number of integer compositions of n that are not the first sums of any finite nonnegative sequence. | [
"0",
"0",
"0",
"0",
"1",
"3",
"11",
"28",
"76",
"178",
"429",
"957",
"2167",
"4686",
"10220",
"21640",
"46057",
"96091",
"201123",
"415164",
"858748",
"1758834",
"3607109",
"7344997",
"14969263",
"30348574",
"61563612",
"124403736",
"251481889",
"506914707",... | [
"nonn",
"easy",
"new"
] | 11 | 1 | 6 | [
"A008965",
"A011782",
"A070211",
"A342527",
"A357213",
"A390307",
"A390445",
"A390447",
"A390567",
"A390568",
"A390673",
"A390675",
"A390676",
"A390677",
"A390678",
"A390745",
"A390747",
"A391235",
"A391621",
"A391622",
"A391623",
"A391627",
"A391628",
"A391629",
"A39... | null | Gus Wiseman, Jan 05 2026 | 2026-01-15T04:50:44 | oeisdata/seq/A391/A391645.seq | a5a207a48e424fcdaad4deb4c6022151 |
A391646 | a(n) is the least integer k such that the sum of the prime divisors of k, each taken modulo its exponent in the prime factorization of k, equals n. | [
"1",
"9",
"8",
"72",
"1000",
"648",
"16200",
"81000",
"1125000",
"38896200",
"10125000",
"496125000",
"3735591048",
"24310125000"
] | [
"nonn",
"more"
] | 47 | 0 | 2 | [
"A000586",
"A001222",
"A001694",
"A008474",
"A343923",
"A391646"
] | null | Jean-Marc Rebert, Dec 15 2025 | 2026-01-04T12:13:36 | oeisdata/seq/A391/A391646.seq | 114cfbf420a012d36b342e7f3b9ac96b |
A391647 | G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^2)^4). | [
"1",
"1",
"5",
"27",
"169",
"1142",
"8119",
"59858",
"453457",
"3508387",
"27605438",
"220222006",
"1777070719",
"14479635755",
"118964104210",
"984458054901",
"8198036158377",
"68648565704822",
"577688470851287",
"4882818680082470",
"41435273356227698",
"352880834583149468... | [
"nonn"
] | 14 | 0 | 3 | [
"A002294",
"A321798",
"A391647",
"A391648",
"A391650"
] | null | Seiichi Manyama, Dec 15 2025 | 2025-12-20T02:55:38 | oeisdata/seq/A391/A391647.seq | dca5073ea4af2c9500e1dab262911a09 |
A391648 | G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^3)^4). | [
"1",
"1",
"5",
"31",
"225",
"1772",
"14735",
"127300",
"1131437",
"10278926",
"95024232",
"891017275",
"8453889679",
"81011181979",
"782933498692",
"7622492479365",
"74689055831309",
"735991269252676",
"7289000770096762",
"72512181598370752",
"724277117405313212",
"72607411... | [
"nonn"
] | 17 | 0 | 3 | [
"A002294",
"A137958",
"A321798",
"A391647",
"A391648",
"A391651"
] | null | Seiichi Manyama, Dec 15 2025 | 2025-12-20T02:55:35 | oeisdata/seq/A391/A391648.seq | 36b397c4eb63d22b11ae6d24331de13a |
A391649 | G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^3)^2). | [
"1",
"1",
"3",
"14",
"75",
"438",
"2704",
"17356",
"114661",
"774514",
"5324812",
"37137379",
"262112002",
"1868610856",
"13436074970",
"97328988039",
"709609323325",
"5203171782012",
"38345109874752",
"283864224950635",
"2109947626538162",
"15740670860816827",
"117819995... | [
"nonn"
] | 14 | 0 | 3 | [
"A367239",
"A391649"
] | null | Seiichi Manyama, Dec 15 2025 | 2025-12-20T02:55:32 | oeisdata/seq/A391/A391649.seq | 5381f3c7591e71de60a7ed08c135a127 |
A391650 | G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^4)^2). | [
"1",
"1",
"3",
"16",
"97",
"643",
"4514",
"32975",
"248073",
"1908922",
"14954639",
"118872632",
"956360378",
"7772627864",
"63719954171",
"526297294068",
"4375423588669",
"36584932651456",
"307464725457800",
"2595746654110011",
"22004044556019121",
"187216588916896334",
... | [
"nonn"
] | 15 | 0 | 3 | [
"A002294",
"A364723",
"A391647",
"A391650",
"A391651"
] | null | Seiichi Manyama, Dec 15 2025 | 2025-12-20T06:30:18 | oeisdata/seq/A391/A391650.seq | f1ab6275b894987e765db3b64bed00a6 |
A391651 | G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)^4)^3). | [
"1",
"1",
"4",
"25",
"179",
"1401",
"11599",
"99892",
"885728",
"8031766",
"74139566",
"694337159",
"6581077628",
"63009948015",
"608507552940",
"5920491082743",
"57979180807909",
"571045632036521",
"5652923643424030",
"56213838501374893",
"561282305297609701",
"56249231257... | [
"nonn"
] | 17 | 0 | 3 | [
"A002293",
"A002294",
"A137957",
"A161797",
"A364723",
"A367239",
"A391648",
"A391650",
"A391651"
] | null | Seiichi Manyama, Dec 15 2025 | 2025-12-20T06:30:21 | oeisdata/seq/A391/A391651.seq | 2a29592e40d56294e6b248806401ef9b |
A391652 | Number of Fibonacci words of length n. | [
"1",
"2",
"5",
"17",
"74",
"425",
"3229",
"33220",
"470345",
"9341720",
"264268383",
"10794722906",
"643739177336",
"56566932708500",
"7380551112905534",
"1439114460819357764",
"421668374889302486279",
"186543928451534747013878",
"125120587007134010705365148",
"1277043077152034... | [
"nonn"
] | 19 | 2 | 2 | null | null | Sela Fried, Dec 15 2025 | 2025-12-20T21:43:36 | oeisdata/seq/A391/A391652.seq | 71b013dcd628322e5fa06a4b6ab7d41b |
A391653 | Decimal expansion of the volume of a Dürer's solid with unit shorter edge length. | [
"1",
"4",
"5",
"3",
"0",
"9",
"2",
"0",
"6",
"3",
"4",
"7",
"3",
"7",
"6",
"9",
"1",
"1",
"3",
"2",
"4",
"5",
"1",
"3",
"1",
"3",
"4",
"4",
"3",
"6",
"9",
"3",
"8",
"9",
"0",
"4",
"1",
"1",
"9",
"1",
"2",
"3",
"4",
"3",
"9",
"... | [
"nonn",
"cons",
"easy"
] | 18 | 2 | 2 | [
"A002163",
"A080992",
"A238238",
"A391653",
"A391654",
"A391655",
"A391656",
"A391657"
] | null | Paolo Xausa, Dec 15 2025 | 2025-12-16T09:32:55 | oeisdata/seq/A391/A391653.seq | 439b8ec703dbb9e27eb5d01bda1f6fb1 |
A391654 | Decimal expansion of the surface area of a Dürer's solid with unit shorter edge length. | [
"3",
"4",
"7",
"7",
"5",
"4",
"4",
"4",
"5",
"2",
"1",
"4",
"8",
"3",
"7",
"3",
"3",
"5",
"0",
"6",
"5",
"2",
"9",
"2",
"5",
"7",
"5",
"9",
"7",
"5",
"1",
"9",
"2",
"0",
"3",
"3",
"3",
"2",
"0",
"8",
"8",
"2",
"9",
"0",
"7",
"... | [
"nonn",
"cons",
"easy"
] | 11 | 2 | 1 | [
"A002163",
"A080992",
"A238238",
"A391653",
"A391654",
"A391655",
"A391656",
"A391657"
] | null | Paolo Xausa, Dec 15 2025 | 2025-12-16T09:32:59 | oeisdata/seq/A391/A391654.seq | feabff526f760b7a3176644cde8b39a6 |
A391655 | Decimal expansion of the circumradius of a Dürer's solid with unit shorter edge length. | [
"2",
"0",
"2",
"0",
"2",
"8",
"6",
"9",
"7",
"9",
"6",
"9",
"1",
"8",
"2",
"4",
"8",
"6",
"7",
"4",
"4",
"1",
"1",
"2",
"3",
"4",
"0",
"1",
"1",
"4",
"4",
"7",
"6",
"8",
"4",
"3",
"8",
"4",
"0",
"5",
"3",
"0",
"8",
"6",
"2",
"... | [
"nonn",
"cons",
"easy"
] | 9 | 1 | 1 | [
"A002163",
"A080992",
"A238238",
"A391653",
"A391654",
"A391655",
"A391656",
"A391657"
] | null | Paolo Xausa, Dec 15 2025 | 2025-12-16T09:32:36 | oeisdata/seq/A391/A391655.seq | c7d2a934b5caca3746c1dcb103079ace |
A391656 | Decimal expansion of the dihedral angle, in radians, between two adjacent pentagonal faces (meeting at their longest edge) in a Dürer's solid. | [
"1",
"8",
"0",
"9",
"1",
"1",
"3",
"7",
"8",
"8",
"6",
"0",
"4",
"7",
"6",
"2",
"7",
"2",
"8",
"2",
"5",
"4",
"6",
"3",
"3",
"5",
"9",
"1",
"3",
"2",
"3",
"9",
"1",
"7",
"4",
"4",
"2",
"8",
"6",
"2",
"1",
"8",
"9",
"1",
"2",
"... | [
"nonn",
"cons",
"easy"
] | 8 | 1 | 2 | [
"A002163",
"A080992",
"A238238",
"A391653",
"A391654",
"A391655",
"A391656",
"A391657"
] | null | Paolo Xausa, Dec 16 2025 | 2025-12-16T09:32:32 | oeisdata/seq/A391/A391656.seq | 62754b0b37e85670f185b6ed01cb8660 |
A391657 | Decimal expansion of the dihedral angle, in radians, between a pentagonal face and a triangular face in a Dürer's solid. | [
"2",
"0",
"0",
"3",
"6",
"5",
"7",
"1",
"9",
"4",
"9",
"7",
"7",
"0",
"5",
"8",
"5",
"4",
"3",
"0",
"8",
"3",
"1",
"9",
"8",
"4",
"4",
"2",
"6",
"4",
"3",
"0",
"4",
"6",
"4",
"8",
"8",
"3",
"5",
"9",
"0",
"0",
"3",
"0",
"4",
"... | [
"nonn",
"cons",
"easy"
] | 11 | 1 | 1 | [
"A010476",
"A080992",
"A238238",
"A391653",
"A391654",
"A391655",
"A391656",
"A391657"
] | null | Paolo Xausa, Dec 16 2025 | 2025-12-16T09:32:29 | oeisdata/seq/A391/A391657.seq | b1485c27856f6483587c77e9a20c2319 |
A391660 | Square array read by antidiagonals: T(n,k) is the Kruskal-Macaulay function K_n of degree n evaluated at k. | [
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"3",
"3",
"0",
"1",
"3",
"5",
"4",
"0",
"1",
"4",
"6",
"7",
"5",
"0",
"1",
"4",
"6",
"9",
"9",
"6",
"0",
"1",
"4",
"8",
"10",
"12",
"11",
"7",
"0",
"1",
"5",
"9",
"10",
"14",
"15",
"13",
"8",
"... | [
"nonn",
"tabl"
] | 7 | 1 | 5 | [
"A003057",
"A057427",
"A123572",
"A123573",
"A123574",
"A391660",
"A391661",
"A391662"
] | null | Pontus von Brömssen, Dec 15 2025 | 2025-12-16T09:32:16 | oeisdata/seq/A391/A391660.seq | eeb84f133a40a36a50a5ee6dd12bde78 |
A391661 | Square array read by antidiagonals: T(n,k) is the Kruskal-Macaulay function L_n of degree n evaluated at k. | [
"0",
"0",
"0",
"1",
"0",
"0",
"3",
"0",
"0",
"0",
"6",
"1",
"0",
"0",
"0",
"10",
"1",
"0",
"0",
"0",
"0",
"15",
"2",
"1",
"0",
"0",
"0",
"0",
"21",
"4",
"1",
"0",
"0",
"0",
"0",
"0",
"28",
"4",
"1",
"1",
"0",
"0",
"0",
"0",
"0",... | [
"nonn",
"tabl"
] | 6 | 1 | 7 | [
"A000217",
"A111138",
"A123575",
"A123576",
"A123577",
"A391660",
"A391661",
"A391662"
] | null | Pontus von Brömssen, Dec 15 2025 | 2025-12-16T09:32:20 | oeisdata/seq/A391/A391661.seq | 69e1e2abab6ddbd80f5cd700af00b811 |
A391662 | Square array read by antidiagonals: T(n,k) is the Kruskal-Macaulay function M_n of degree n evaluated at k. | [
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"1",
"0",
"1",
"2",
"2",
"1",
"0",
"1",
"3",
"3",
"2",
"1",
"0",
"1",
"3",
"3",
"3",
"2",
"1",
"0",
"1",
"3",
"4",
"4",
"3",
"2",
"1",
"0",
"1",
"4",
"5",
"4",
"4",
"3",
"2",
"1",
"0",
"... | [
"nonn",
"tabl"
] | 6 | 1 | 8 | [
"A057427",
"A123578",
"A123579",
"A123580",
"A123731",
"A391660",
"A391661",
"A391662"
] | null | Pontus von Brömssen, Dec 15 2025 | 2025-12-16T09:32:24 | oeisdata/seq/A391/A391662.seq | d3389ff1c1f3e305612ad2b38b4f9a9b |
A391663 | Numbers k such that (23^k - 5^k)/18 is prime. | [
"53",
"137",
"719",
"2957",
"5483",
"8147"
] | [
"nonn",
"hard",
"more"
] | 7 | 1 | 1 | [
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A229542",
"A375161",
"A375236",
"A377031",
"A391663"
] | null | Robert Price, Dec 15 2025 | 2025-12-16T09:32:06 | oeisdata/seq/A391/A391663.seq | ea803a410ae855335037df348c970f29 |
A391664 | Number of permutations p of [2*n] satisfying Sum_{i=1..2*n} (p(i)-i)^2 = 2*n. | [
"1",
"1",
"1",
"9",
"47",
"177",
"691",
"3001",
"13274",
"57912",
"252497",
"1109961",
"4908590",
"21763925",
"96687202",
"430528955",
"1921312439",
"8589901368",
"38463789496",
"172476073461",
"774406324182",
"3481116734538",
"15664952999940",
"70560301836647",
"3181... | [
"nonn"
] | 10 | 0 | 4 | [
"A175929",
"A390749",
"A391511",
"A391664"
] | null | Alois P. Heinz, Dec 15 2025 | 2025-12-17T15:54:04 | oeisdata/seq/A391/A391664.seq | 8ef5f0770612a345bf176fb4d55fee50 |
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