Datasets:
christopher
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oeis

Dataset card Data Studio Files
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 Community
2
sequence_id
stringlengths
7
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sequence
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348
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listlengths
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score
int64
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2.47k
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int64
-14,827
666,262,453B
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int64
0
635M
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cross_references
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2026-01-19 02:46:49
filename
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29
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32
32
A001601
a(n) = 2*a(n-1)^2 - 1, if n>1. a(0)=1, a(1)=3.
[ "1", "3", "17", "577", "665857", "886731088897", "1572584048032918633353217", "4946041176255201878775086487573351061418968498177" ]
[ "nonn", "easy", "nice", "frac" ]
119
0
2
[ "A001333", "A001601", "A003423", "A051009" ]
[ "M3042", "N1234" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001601.seq
738c802f6c0e16d9a0bbc06b2fca600c
A001602
Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).
[ "3", "4", "5", "8", "10", "7", "9", "18", "24", "14", "30", "19", "20", "44", "16", "27", "58", "15", "68", "70", "37", "78", "84", "11", "49", "50", "104", "36", "27", "19", "128", "130", "69", "46", "37", "50", "79", "164", "168", "87",...
[ "nonn", "nice" ]
167
1
1
[ "A001177", "A001602", "A051694", "A086597", "A194363" ]
[ "M2310", "N0912" ]
N. J. A. Sloane
2025-11-13T16:05:15
oeisdata/seq/A001/A001602.seq
a24d621b8eab1146972b9ba77c414c5a
A001603
Odd-indexed terms of A124296.
[ "1", "11", "101", "781", "5611", "39161", "270281", "1857451", "12744061", "87382901", "599019851", "4105974961", "28143378001", "192899171531", "1322154751061", "9062194370461", "62113232767531", "425730505493801", "2918000490238361", "20000273409331051", "137083914639998701...
[ "nonn", "easy" ]
48
0
2
[ "A001603", "A001604", "A124296", "A124297" ]
[ "M4801", "N2051" ]
N. J. A. Sloane
2023-06-25T02:37:26
oeisdata/seq/A001/A001603.seq
09c06b27070b0b9ace2d2f9060c7a5e8
A001604
Odd-indexed terms of A124297.
[ "11", "31", "151", "911", "5951", "40051", "272611", "1863551", "12760031", "87424711", "599129311", "4106261531", "28144128251", "192901135711", "1322159893351", "9062207833151", "62113268013311", "425730597768451", "2918000731816531", "20000274041790911", "13708391629580011...
[ "nonn", "easy" ]
51
0
1
[ "A001603", "A001604", "A124296", "A124297" ]
[ "M4785", "N2042" ]
N. J. A. Sloane
2023-06-25T02:38:55
oeisdata/seq/A001/A001604.seq
42c42f67ca7590ec88054d147adc62e2
A001605
Indices of prime Fibonacci numbers.
[ "3", "4", "5", "7", "11", "13", "17", "23", "29", "43", "47", "83", "131", "137", "359", "431", "433", "449", "509", "569", "571", "2971", "4723", "5387", "9311", "9677", "14431", "25561", "30757", "35999", "37511", "50833", "81839", "104911", "130...
[ "nonn", "hard", "nice" ]
216
1
1
[ "A000045", "A001578", "A001605", "A005478", "A046022", "A080345", "A086597", "A117595", "A303215" ]
[ "M2309", "N0911" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001605.seq
018d0f2d02c351cfb2daee3213de23c7
A001606
Indices of prime Lucas numbers.
[ "0", "2", "4", "5", "7", "8", "11", "13", "16", "17", "19", "31", "37", "41", "47", "53", "61", "71", "79", "113", "313", "353", "503", "613", "617", "863", "1097", "1361", "4787", "4793", "5851", "7741", "8467", "10691", "12251", "13963", "144...
[ "nonn", "hard", "nice" ]
98
1
2
[ "A000032", "A000204", "A001605", "A001606", "A005479", "A076697", "A080327" ]
[ "M0961", "N0358" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001606.seq
82c6980925ac8da3d5c009bc4b451e36
A001607
a(n) = -a(n-1) - 2*a(n-2).
[ "0", "1", "-1", "-1", "3", "-1", "-5", "7", "3", "-17", "11", "23", "-45", "-1", "91", "-89", "-93", "271", "-85", "-457", "627", "287", "-1541", "967", "2115", "-4049", "-181", "8279", "-7917", "-8641", "24475", "-7193", "-41757", "56143", "27371"...
[ "sign", "easy" ]
97
0
5
[ "A001607", "A002249", "A077020", "A077021", "A107920", "A167433", "A169998", "A172250" ]
[ "M2225", "N0883" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001607.seq
6b130f6875d1002c79ac804158901adf
A001608
Perrin sequence (or Perrin numbers, or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.
[ "3", "0", "2", "3", "2", "5", "5", "7", "10", "12", "17", "22", "29", "39", "51", "68", "90", "119", "158", "209", "277", "367", "486", "644", "853", "1130", "1497", "1983", "2627", "3480", "4610", "6107", "8090", "10717", "14197", "18807", "24...
[ "nonn", "easy", "nice" ]
478
0
1
[ "A000931", "A001608", "A013998", "A018187", "A109377", "A182097", "A389621", "A389623" ]
[ "M0429", "N0163" ]
N. J. A. Sloane
2025-12-19T22:31:12
oeisdata/seq/A001/A001608.seq
36cee18836cffb769c71ad70bade7f26
A001609
a(1) = a(2) = 1, a(3) = 4; thereafter a(n) = a(n-1) + a(n-3).
[ "1", "1", "4", "5", "6", "10", "15", "21", "31", "46", "67", "98", "144", "211", "309", "453", "664", "973", "1426", "2090", "3063", "4489", "6579", "9642", "14131", "20710", "30352", "44483", "65193", "95545", "140028", "205221", "300766", "440794",...
[ "nonn", "easy" ]
104
1
3
[ "A000079", "A000204", "A000930", "A001609", "A003269", "A003520", "A005708", "A005709", "A005710", "A014097", "A049064", "A049194", "A218439" ]
[ "M3240", "N1308" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001609.seq
54b18614f94f72fc905b557d6a151326
A001610
a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 2.
[ "0", "2", "3", "6", "10", "17", "28", "46", "75", "122", "198", "321", "520", "842", "1363", "2206", "3570", "5777", "9348", "15126", "24475", "39602", "64078", "103681", "167760", "271442", "439203", "710646", "1149850", "1860497", "3010348", "4870846",...
[ "nonn", "easy", "hear" ]
181
0
2
[ "A000032", "A000071", "A000126", "A000204", "A000296", "A001610", "A001644", "A032190", "A169985", "A174625", "A306357" ]
[ "M0764", "N0291" ]
N. J. A. Sloane
2025-11-20T13:24:17
oeisdata/seq/A001/A001610.seq
c5909306a2fbbaf91826a77003dea9d9
A001611
a(n) = Fibonacci(n) + 1.
[ "1", "2", "2", "3", "4", "6", "9", "14", "22", "35", "56", "90", "145", "234", "378", "611", "988", "1598", "2585", "4182", "6766", "10947", "17712", "28658", "46369", "75026", "121394", "196419", "317812", "514230", "832041", "1346270", "2178310", "...
[ "nonn", "easy", "hear" ]
140
0
2
[ "A000045", "A000071", "A001611", "A001911", "A002062", "A006327", "A019863", "A097280", "A097281", "A157725", "A157726", "A157727", "A157728", "A157729", "A160536", "A167616", "A212272", "A242876" ]
[ "M0288", "N0103" ]
N. J. A. Sloane
2024-11-28T11:11:53
oeisdata/seq/A001/A001611.seq
06556c3486cdde457541693607518e44
A001612
a(n) = a(n-1) + a(n-2) - 1 for n > 1, a(0)=3, a(1)=2.
[ "3", "2", "4", "5", "8", "12", "19", "30", "48", "77", "124", "200", "323", "522", "844", "1365", "2208", "3572", "5779", "9350", "15128", "24477", "39604", "64080", "103683", "167762", "271444", "439205", "710648", "1149852", "1860499", "3010350", "48...
[ "nonn", "easy", "hear" ]
113
0
1
[ "A000032", "A000071", "A001612", "A274017" ]
[ "M0974", "N0364" ]
N. J. A. Sloane
2025-06-01T03:16:45
oeisdata/seq/A001/A001612.seq
8e15154ab9ed018aaa2f1fe65c060ddc
A001613
Delete all odd digits from n.
[ "0", "0", "2", "0", "4", "0", "6", "0", "8", "0", "0", "0", "2", "0", "4", "0", "6", "0", "8", "0", "20", "2", "22", "2", "24", "2", "26", "2", "28", "2", "0", "0", "2", "0", "4", "0", "6", "0", "8", "0", "40", "4", "42", "4", "...
[ "base", "nonn" ]
8
0
3
null
null
N. J. A. Sloane
2022-02-01T23:33:50
oeisdata/seq/A001/A001613.seq
fad2302dc79a77a3aac1c1336acc4f93
A001614
Connell sequence: 1 odd, 2 even, 3 odd, ...
[ "1", "2", "4", "5", "7", "9", "10", "12", "14", "16", "17", "19", "21", "23", "25", "26", "28", "30", "32", "34", "36", "37", "39", "41", "43", "45", "47", "49", "50", "52", "54", "56", "58", "60", "62", "64", "65", "67", "69", "71", "7...
[ "nonn", "easy", "nice", "tabl" ]
105
1
2
[ "A000290", "A000292", "A001614", "A002522", "A008865", "A014132", "A023531", "A028347", "A028878", "A028884", "A054569", "A057211", "A058187", "A069778", "A117384", "A117619", "A117950", "A117951", "A118011", "A118012", "A154533", "A190716", "A190717", "A190718" ]
[ "M0962", "N0359" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001614.seq
d5ca0b8342b978e07b3321c79f41e5ad
A001615
Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p).
[ "1", "3", "4", "6", "6", "12", "8", "12", "12", "18", "12", "24", "14", "24", "24", "24", "18", "36", "20", "36", "32", "36", "24", "48", "30", "42", "36", "48", "30", "72", "32", "48", "48", "54", "48", "72", "38", "60", "56", "72", "4...
[ "nonn", "easy", "core", "nice", "mult" ]
306
1
2
[ "A000082", "A000203", "A001615", "A002110", "A003050", "A003051", "A019269", "A027748", "A033196", "A034444", "A054345", "A063659", "A065958", "A065959", "A065960", "A082020", "A082695", "A124010", "A156303", "A160889", "A160891", "A173290", "A175732", "A175836", "A20...
[ "M2315", "N0915" ]
N. J. A. Sloane
2025-11-08T03:34:50
oeisdata/seq/A001/A001615.seq
222b526f32bf50a103e64682d8b6abe9
A001616
Number of parabolic vertices of Gamma_0(n).
[ "1", "2", "2", "3", "2", "4", "2", "4", "4", "4", "2", "6", "2", "4", "4", "6", "2", "8", "2", "6", "4", "4", "2", "8", "6", "4", "6", "6", "2", "8", "2", "8", "4", "4", "4", "12", "2", "4", "4", "8", "2", "8", "2", "6", "8", ...
[ "nonn", "easy", "nice", "mult" ]
72
1
2
[ "A000010", "A001616", "A027748", "A027750", "A124010" ]
[ "M0247", "N0087" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001616.seq
c14991b4e63e25ec22d99e2036c4ec2e
A001617
Genus of modular group Gamma_0(n). Or, genus of modular curve X_0(n).
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "1", "2", "2", "1", "0", "2", "1", "2", "2", "3", "2", "1", "3", "3", "3", "1", "2", "4", "3", "3", "3", "5", "3", "4", "3", "...
[ "nonn", "easy", "nice" ]
79
1
22
[ "A000086", "A000089", "A001615", "A001616", "A001617", "A054728", "A091401", "A091403", "A091404" ]
[ "M0188", "N0069" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001617.seq
b59324bb264dae5f66632d90a6542789
A001618
Nearest integer to 2*n*log(n).
[ "0", "0", "3", "7", "11", "16", "22", "27", "33", "40", "46", "53", "60", "67", "74", "81", "89", "96", "104", "112", "120", "128", "136", "144", "153", "161", "169", "178", "187", "195", "204", "213", "222", "231", "240", "249", "258", "267"...
[ "nonn", "easy" ]
31
0
3
null
[ "M2623", "N1038" ]
N. J. A. Sloane
2025-01-23T16:53:00
oeisdata/seq/A001/A001618.seq
25dbad7fda3ae73e8235c1f88769b40d
A001619
Number of letters in English name for n increases at these numbers.
[ "1", "3", "11", "13", "17", "21", "23", "73", "101", "103", "111", "113", "117", "121", "123", "173", "323", "373", "1103", "1111", "1113", "1117", "1121", "1123", "1173", "1323", "1373", "3323", "3373", "11373", "13323", "13373", "17373", "21373", ...
[ "word", "nonn" ]
10
1
2
null
null
N. J. A. Sloane
2022-02-01T23:34:09
oeisdata/seq/A001/A001619.seq
895303f466effd6b501d2d62a605c41b
A001620
Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma.
[ "5", "7", "7", "2", "1", "5", "6", "6", "4", "9", "0", "1", "5", "3", "2", "8", "6", "0", "6", "0", "6", "5", "1", "2", "0", "9", "0", "0", "8", "2", "4", "0", "2", "4", "3", "1", "0", "4", "2", "1", "5", "9", "3", "3", "5", "...
[ "nonn", "cons", "nice" ]
459
0
1
[ "A001620", "A002852", "A073004", "A075266", "A082633", "A086279", "A086280", "A086281", "A086282", "A094640", "A183141", "A183167", "A183206", "A184853", "A184854", "A199332", "A231095", "A252898", "A262235", "A262382", "A262383", "A262384", "A262385", "A262386", "A26...
[ "M3755", "N1532" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001620.seq
ba11c4e75d50a135959b6f295bce4c39
A001621
a(n) = n*(n + 1)*(n^2 + n + 2)/4.
[ "0", "2", "12", "42", "110", "240", "462", "812", "1332", "2070", "3080", "4422", "6162", "8372", "11130", "14520", "18632", "23562", "29412", "36290", "44310", "53592", "64262", "76452", "90300", "105950", "123552", "143262", "165242", "189660", "216690",...
[ "nonn", "easy" ]
40
0
2
[ "A000124", "A000217", "A001621", "A002817", "A034262", "A058919", "A092365" ]
null
N. J. A. Sloane
2022-10-08T16:39:33
oeisdata/seq/A001/A001621.seq
fd03941a3138800275cd257f04ca8e74
A001622
Decimal expansion of golden ratio phi (or tau) = (1 + sqrt(5))/2.
[ "1", "6", "1", "8", "0", "3", "3", "9", "8", "8", "7", "4", "9", "8", "9", "4", "8", "4", "8", "2", "0", "4", "5", "8", "6", "8", "3", "4", "3", "6", "5", "6", "3", "8", "1", "1", "7", "7", "2", "0", "3", "0", "9", "1", "7", "...
[ "nonn", "cons", "core", "nice", "easy" ]
604
1
2
[ "A000012", "A000032", "A000045", "A001622", "A002163", "A006497", "A080039", "A094874", "A102208", "A102769", "A104457", "A131595", "A134973", "A139339", "A145996", "A188635", "A192222", "A192223", "A197762", "A302973", "A303069", "A304022" ]
[ "M4046", "N1679" ]
N. J. A. Sloane
2026-01-03T21:10:40
oeisdata/seq/A001/A001622.seq
353c46b981cd581f8431db418c692d59
A001623
Number of 3 X n reduced (normalized) Latin rectangles.
[ "1", "4", "46", "1064", "35792", "1673792", "103443808", "8154999232", "798030483328", "94866122760704", "13460459852344064", "2246551018310998016", "435626600453967929344", "97108406689489312301056", "24658059294992101453262848", "7075100096781964808223653888", "22777100957067794800...
[ "nonn", "nice" ]
51
3
2
[ "A001009", "A001623" ]
[ "M3682", "N1502" ]
N. J. A. Sloane
2016-11-09T15:03:10
oeisdata/seq/A001/A001623.seq
39c53fad201ce5c46130a2862bf2bddd
A001624
Related to Latin rectangles.
[ "1", "5", "58", "1274", "41728", "1912112", "116346400", "9059742176", "877746364288", "103483282967936", "14581464284095744", "2419278174185319680", "466730664414683625472", "103580258158369503481856", "26198788829773597178540032" ]
[ "nonn" ]
20
2
2
null
[ "M4017", "N1665" ]
N. J. A. Sloane
2022-02-01T23:34:22
oeisdata/seq/A001/A001624.seq
111c3e1876571bde7bada00180e8f3b8
A001625
Related to Latin rectangles.
[ "2", "4", "60", "1276", "41888", "1916064", "116522048", "9069595840", "878460379392", "103547791177216", "14588580791234048", "2420219602973093376", "466877775127725240320", "103607067936116866084864", "26204424894484840874483712" ]
[ "nonn" ]
20
2
1
null
[ "M1304", "N0500" ]
N. J. A. Sloane
2022-02-01T23:36:20
oeisdata/seq/A001/A001625.seq
e18eebecc39bc4c5950a1b70f9ac4e0d
A001626
Number of 3-line Latin rectangles.
[ "0", "0", "2", "36", "840", "29680", "1429920", "90318144", "7237943552", "717442928640", "86171602072320", "12331048749268480", "2072725870491859968", "404352831489304049664", "90605920564322676531200", "23110943021722435879157760", "6657484407493222296916131840" ]
[ "nonn" ]
23
1
3
[ "A000186", "A001626" ]
[ "M2158", "N0860" ]
N. J. A. Sloane
2022-02-01T23:36:40
oeisdata/seq/A001/A001626.seq
591301c4e0a37d76746dad0bbb845845
A001627
Related to Latin rectangles.
[ "1", "0", "2", "44", "1008", "34432", "1629280", "101401344", "8030787968", "788377273856", "93933191303424", "13350759115563520", "2231133728986759168", "433075048506207645696", "96617322164029448916992", "24549315871469898190266368", "7047652261245574026565877760" ]
[ "nonn" ]
18
1
3
null
[ "M2165", "N0862" ]
N. J. A. Sloane
2022-02-01T23:36:59
oeisdata/seq/A001/A001627.seq
b8565adc4c7398f36a3f7b14acb9a516
A001628
Convolved Fibonacci numbers.
[ "1", "3", "9", "22", "51", "111", "233", "474", "942", "1836", "3522", "6666", "12473", "23109", "42447", "77378", "140109", "252177", "451441", "804228", "1426380", "2519640", "4434420", "7777860", "13599505", "23709783", "41225349", "71501422", "123723351", ...
[ "nonn", "easy" ]
156
0
2
[ "A001628", "A037027", "A055243", "A291915" ]
[ "M2789", "N1124" ]
N. J. A. Sloane, Simon Plouffe
2025-11-26T15:59:31
oeisdata/seq/A001/A001628.seq
c13ee4b864262e0070f565fb10730d63
A001629
Self-convolution of Fibonacci numbers.
[ "0", "0", "1", "2", "5", "10", "20", "38", "71", "130", "235", "420", "744", "1308", "2285", "3970", "6865", "11822", "20284", "34690", "59155", "100610", "170711", "289032", "488400", "823800", "1387225", "2332418", "3916061", "6566290", "10996580", "18...
[ "nonn", "easy", "nice" ]
435
0
4
[ "A000032", "A000045", "A001628", "A001629", "A006478", "A010049", "A037027", "A055244", "A058071", "A134510", "A134836", "A214178" ]
[ "M1377", "N0537" ]
N. J. A. Sloane
2025-12-24T15:08:22
oeisdata/seq/A001/A001629.seq
4697a0bed5481c9e428a60a834345461
A001630
Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=a(1)=0, a(2)=1, a(3)=2.
[ "0", "0", "1", "2", "3", "6", "12", "23", "44", "85", "164", "316", "609", "1174", "2263", "4362", "8408", "16207", "31240", "60217", "116072", "223736", "431265", "831290", "1602363", "3088654", "5953572", "11475879", "22120468", "42638573", "82188492", ...
[ "nonn", "easy" ]
115
0
4
[ "A000032", "A001630", "A007283", "A054886", "A078042", "A096231", "A163876", "A179070", "A265057", "A265058", "A265059", "A265060", "A265061", "A265062", "A265063", "A265064", "A265065", "A265066", "A265067", "A265068", "A265069", "A265070", "A265071", "A265072", "A26...
[ "M0795", "N0301" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001630.seq
ceea98bc609d1a5346e6dfa9eb8dd7fb
A001631
Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with initial conditions a(0..3) = (0, 0, 1, 0).
[ "0", "0", "1", "0", "1", "2", "4", "7", "14", "27", "52", "100", "193", "372", "717", "1382", "2664", "5135", "9898", "19079", "36776", "70888", "136641", "263384", "507689", "978602", "1886316", "3635991", "7008598", "13509507", "26040412", "50194508", ...
[ "nonn", "easy" ]
129
0
6
[ "A000078", "A000288", "A000336", "A001631" ]
[ "M1081", "N0410" ]
N. J. A. Sloane
2025-12-08T02:04:14
oeisdata/seq/A001/A001631.seq
194d5a2519776a4697811cb750c53910
A001632
Smallest prime p such that there is a gap of 2n between p and previous prime.
[ "5", "11", "29", "97", "149", "211", "127", "1847", "541", "907", "1151", "1693", "2503", "2999", "4327", "5623", "1361", "9587", "30631", "19373", "16183", "15727", "81509", "28277", "31957", "19661", "35671", "82129", "44351", "43391", "34123", "89753"...
[ "nonn", "nice", "easy" ]
38
1
1
[ "A000230", "A001632", "A002386" ]
[ "M3812", "N1560" ]
N. J. A. Sloane
2021-12-19T10:02:50
oeisdata/seq/A001/A001632.seq
111310f669e479eb57c8ff017cafc037
A001633
Numbers with an odd number of digits.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "120", "121", "122", "123", "124", "125", "126", "12...
[ "nonn", "base", "easy" ]
30
1
3
[ "A001633", "A001637", "A055642" ]
null
N. J. A. Sloane
2022-11-29T12:24:51
oeisdata/seq/A001/A001633.seq
3b435dd0dd09b7ff0213fbb82adcf687
A001634
a(n) = a(n-2) + a(n-3) + a(n-4), with initial values a(0) = 0, a(1) = 2, a(2) = 3, a(3) = 6.
[ "0", "2", "3", "6", "5", "11", "14", "22", "30", "47", "66", "99", "143", "212", "308", "454", "663", "974", "1425", "2091", "3062", "4490", "6578", "9643", "14130", "20711", "30351", "44484", "65192", "95546", "140027", "205222", "300765", "440795",...
[ "nonn", "easy", "nice" ]
59
0
2
[ "A001634", "A013979", "A107458" ]
[ "M0746", "N0281" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001634.seq
5d32cf07a2d826db94e5302f86135a14
A001635
A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-6), n >= 7.
[ "0", "2", "3", "6", "10", "11", "21", "30", "48", "72", "110", "171", "260", "401", "613", "942", "1445", "2216", "3401", "5216", "8004", "12278", "18837", "28899", "44335", "68018", "104349", "160089", "245601", "376791", "578057", "886830", "1360538"...
[ "nonn" ]
56
1
2
[ "A000129", "A001635" ]
[ "M0762", "N0289" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001635.seq
a713a7863c01ea2f2d08b9c31d7b0b90
A001636
A Fielder sequence: a(n) = a(n-1) + a(n-2) - a(n-7), n >= 8.
[ "0", "2", "3", "6", "10", "17", "21", "38", "57", "92", "143", "225", "351", "555", "868", "1366", "2142", "3365", "5282", "8296", "13023", "20451", "32108", "50417", "79160", "124295", "195159", "306431", "481139", "755462", "1186184", "1862486", "292...
[ "nonn" ]
46
1
2
[ "A001636", "A013983" ]
[ "M0763", "N0290" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001636.seq
cb6a42370f005053b303c607f1fb0b54
A001637
Numbers with an even number of digits.
[ "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49"...
[ "nonn", "base", "easy" ]
29
1
1
[ "A001633", "A001637", "A055642" ]
null
N. J. A. Sloane
2022-11-11T08:07:53
oeisdata/seq/A001/A001637.seq
ce9d42304bd0d02d571de97b48a3f140
A001638
A Fielder sequence: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
[ "4", "1", "1", "4", "9", "11", "16", "29", "49", "76", "121", "199", "324", "521", "841", "1364", "2209", "3571", "5776", "9349", "15129", "24476", "39601", "64079", "103684", "167761", "271441", "439204", "710649", "1149851", "1860496", "3010349", "48...
[ "nonn", "easy" ]
79
0
1
[ "A000032", "A001609", "A001634", "A001636", "A001638", "A001645", "A001648", "A001649" ]
[ "M3351", "N1348" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001638.seq
e1d44abf5993bd15a34adf372f207d43
A001639
A Fielder sequence. a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5), n >= 6.
[ "1", "1", "4", "9", "16", "22", "36", "65", "112", "186", "309", "522", "885", "1492", "2509", "4225", "7124", "12010", "20236", "34094", "57453", "96823", "163163", "274946", "463316", "780755", "1315687", "2217112", "3736129", "6295887", "10609441", "1...
[ "nonn" ]
46
1
3
[ "A000570", "A001639" ]
[ "M3353", "N1349" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001639.seq
c773a9fbea451ce855216aadac126ff4
A001640
A Fielder sequence.
[ "1", "1", "4", "9", "16", "28", "43", "73", "130", "226", "386", "660", "1132", "1947", "3349", "5753", "9878", "16966", "29147", "50074", "86020", "147764", "253829", "436036", "749041", "1286728", "2210377", "3797047", "6522681", "11204863", "19248056", ...
[ "nonn" ]
40
1
3
null
[ "M3358", "N1352" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001640.seq
8a88c200545e521149f22ef2e617bd4b
A001641
A Fielder sequence: a(n) = a(n-1) + a(n-2) + a(n-4).
[ "1", "3", "4", "11", "16", "30", "50", "91", "157", "278", "485", "854", "1496", "2628", "4609", "8091", "14196", "24915", "43720", "76726", "134642", "236283", "414645", "727654", "1276941", "2240878", "3932464", "6900996", "12110401", "21252275", "372951...
[ "nonn", "easy" ]
67
1
2
[ "A001609", "A001634", "A001636", "A001638", "A001641", "A001645", "A001648", "A001649", "A060945" ]
[ "M2364", "N0935" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001641.seq
fdd69416c75c2beb0a516d26e92366fb
A001642
A Fielder sequence.
[ "1", "3", "4", "11", "21", "36", "64", "115", "211", "383", "694", "1256", "2276", "4126", "7479", "13555", "24566", "44523", "80694", "146251", "265066", "480406", "870689", "1578040", "2860046", "5183558", "9394699", "17026986", "30859771", "55930361", "...
[ "nonn" ]
47
1
2
null
[ "M2367", "N0937" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001642.seq
50d7f3fe3a28fd35111617a5b55272ed
A001643
A Fielder sequence.
[ "1", "3", "4", "11", "21", "42", "71", "131", "238", "443", "815", "1502", "2757", "5071", "9324", "17155", "31553", "58038", "106743", "196331", "361106", "664183", "1221623", "2246918", "4132721", "7601259", "13980892", "25714875", "47297029", "86992802", ...
[ "nonn" ]
50
1
2
[ "A001643", "A001644" ]
[ "M2368", "N0938" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001643.seq
1dca69c6f7e35b13ab862c98803e3646
A001644
a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=1, a(2)=3.
[ "3", "1", "3", "7", "11", "21", "39", "71", "131", "241", "443", "815", "1499", "2757", "5071", "9327", "17155", "31553", "58035", "106743", "196331", "361109", "664183", "1221623", "2246915", "4132721", "7601259", "13980895", "25714875", "47297029", "8699...
[ "nonn", "easy" ]
307
0
1
[ "A000073", "A001609", "A001634", "A001636", "A001638", "A001644", "A001645", "A001648", "A001649", "A058265", "A073145", "A073728", "A106293" ]
[ "M2625", "N1040" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001644.seq
dc1247b273cccabf6c11bf6889579a8c
A001645
A Fielder sequence.
[ "1", "3", "7", "11", "26", "45", "85", "163", "304", "578", "1090", "2057", "3888", "7339", "13862", "26179", "49437", "93366", "176321", "332986", "628852", "1187596", "2242800", "4235569", "7998951", "15106172", "28528288", "53876211", "101746240", "192149...
[ "nonn", "easy" ]
41
1
2
[ "A001609", "A001634", "A001636", "A001638", "A001645", "A001648", "A001649" ]
[ "M2626", "N1041" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001645.seq
1c2ef021d31edac74782bf9e2105d554
A001646
Number of self-dual codes of length 2n over GF(4).
[ "1", "1", "1", "2", "3", "5", "10", "21", "55", "245", "3427" ]
[ "nonn", "hard", "more" ]
21
0
4
null
null
N. J. A. Sloane
2021-09-14T01:11:56
oeisdata/seq/A001/A001646.seq
335d14cc6b0bcd0d54839950719695cf
A001647
Number of indecomposable self-dual codes of length 2n over GF(4).
[ "1", "0", "1", "1", "2", "4", "10", "31" ]
[ "nonn", "hard", "nice", "more" ]
15
1
5
null
null
N. J. A. Sloane
2022-03-12T21:41:15
oeisdata/seq/A001/A001647.seq
72b4dae58ac35e3aebb36176d4364cb1
A001648
Tetranacci numbers A073817 without the leading term 4.
[ "1", "3", "7", "15", "26", "51", "99", "191", "367", "708", "1365", "2631", "5071", "9775", "18842", "36319", "70007", "134943", "260111", "501380", "966441", "1862875", "3590807", "6921503", "13341626", "25716811", "49570747", "95550687", "184179871", "3550...
[ "nonn", "easy" ]
73
1
2
[ "A000288", "A001648", "A073817" ]
[ "M2648", "N1055" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001648.seq
7315096d7f3477a049a43b32fa944c03
A001649
A Fielder sequence.
[ "1", "3", "7", "15", "26", "57", "106", "207", "403", "788", "1530", "2985", "5812", "11322", "22052", "42959", "83675", "162993", "317491", "618440", "1204651", "2346534", "4570791", "8903409", "17342876", "33782050", "65803777", "128178646", "249678140", "...
[ "nonn" ]
38
1
2
null
[ "M2649", "N1056" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001649.seq
8094d6840bffa1d44a7ff260aed0ed0d
A001650
k appears k times (k odd).
[ "1", "3", "3", "3", "5", "5", "5", "5", "5", "7", "7", "7", "7", "7", "7", "7", "9", "9", "9", "9", "9", "9", "9", "9", "9", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "11", "13", "13", "13", "13", "13", "13", "13",...
[ "nonn", "easy" ]
41
1
2
[ "A000122", "A001650", "A001670", "A003881", "A111650", "A131507", "A193832" ]
null
N. J. A. Sloane
2024-11-24T01:49:37
oeisdata/seq/A001/A001650.seq
d844f0ad12bd162d9f0203ceb0c8d688
A001651
Numbers not divisible by 3.
[ "1", "2", "4", "5", "7", "8", "10", "11", "13", "14", "16", "17", "19", "20", "22", "23", "25", "26", "28", "29", "31", "32", "34", "35", "37", "38", "40", "41", "43", "44", "46", "47", "49", "50", "52", "53", "55", "56", "58", "59", "6...
[ "nonn", "easy" ]
307
1
2
[ "A000027", "A000217", "A000292", "A000726", "A000982", "A001082", "A001477", "A001651", "A003105", "A004526", "A005408", "A007494", "A008585", "A008619", "A011655", "A014437", "A026386", "A032766", "A040001", "A047239", "A047257", "A059564", "A073010", "A077043", "A08...
[ "M0957", "N0357" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001651.seq
d4def619665216552c149066014bbdfe
A001652
a(n) = 6*a(n-1) - a(n-2) + 2 with a(0) = 0, a(1) = 3.
[ "0", "3", "20", "119", "696", "4059", "23660", "137903", "803760", "4684659", "27304196", "159140519", "927538920", "5406093003", "31509019100", "183648021599", "1070379110496", "6238626641379", "36361380737780", "211929657785303", "1235216565974040", "7199369738058939", ...
[ "nonn", "easy", "nice" ]
428
0
2
[ "A000129", "A000217", "A001108", "A001109", "A001333", "A001541", "A001542", "A001652", "A001653", "A001921", "A002024", "A002315", "A002378", "A006451", "A029549", "A046090", "A048739", "A053141", "A053142", "A055997", "A075841", "A084159", "A084703", "A089950", "A09...
[ "M3074", "N1247" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001652.seq
91519816815dcaf8f5409d3faf279588
A001653
Numbers k such that 2*k^2 - 1 is a square.
[ "1", "5", "29", "169", "985", "5741", "33461", "195025", "1136689", "6625109", "38613965", "225058681", "1311738121", "7645370045", "44560482149", "259717522849", "1513744654945", "8822750406821", "51422757785981", "299713796309065", "1746860020068409", "10181446324101389",...
[ "nonn", "easy", "nice" ]
494
1
2
[ "A000217", "A000290", "A001109", "A001519", "A001652", "A001653", "A002315", "A002559", "A005054", "A005319", "A046090", "A056220", "A056869", "A069894", "A094954", "A122074", "A188647", "A238379", "A391707" ]
[ "M3955", "N1630" ]
N. J. A. Sloane
2025-12-20T06:30:49
oeisdata/seq/A001/A001653.seq
30d5981ab583cdf04069877c1aae7bf5
A001654
Golden rectangle numbers: F(n) * F(n+1), where F(n) = A000045(n) (Fibonacci numbers).
[ "0", "1", "2", "6", "15", "40", "104", "273", "714", "1870", "4895", "12816", "33552", "87841", "229970", "602070", "1576239", "4126648", "10803704", "28284465", "74049690", "193864606", "507544127", "1328767776", "3478759200", "9107509825", "23843770274", "6242...
[ "nonn", "easy" ]
318
0
3
[ "A000071", "A001654", "A001655", "A001656", "A001657", "A001658", "A005968", "A005969", "A006498", "A007598", "A010048", "A064831", "A067962", "A070550", "A079472", "A080145", "A080239", "A098531", "A098532", "A098533", "A119283", "A128697", "A239798", "A290565" ]
[ "M1606", "N0628" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001654.seq
316d841758a887a8e8cf2c414611a214
A001655
Fibonomial coefficients: a(n) = F(n+1) * F(n+2) * F(n+3)/2, where F() = Fibonacci numbers A000045.
[ "1", "3", "15", "60", "260", "1092", "4641", "19635", "83215", "352440", "1493064", "6324552", "26791505", "113490195", "480752895", "2036500788", "8626757644", "36543528780", "154800876945", "655747029795", "2777789007071", "11766903040368", "49845401197200", "21114850...
[ "nonn", "easy" ]
158
0
2
[ "A000045", "A001655", "A055870", "A065563", "A066258", "A079586", "A114525", "A215037", "A256178", "A363753" ]
[ "M2988", "N1208" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001655.seq
2c0fffe73256a89c6b2ea976c442ffb6
A001656
Fibonomial coefficients.
[ "1", "5", "40", "260", "1820", "12376", "85085", "582505", "3994320", "27372840", "187628376", "1285992240", "8814405145", "60414613805", "414088493560", "2838203264876", "19453338487220", "133335155341960", "913892777190965", "6263914210945105" ]
[ "nonn", "easy" ]
85
0
2
[ "A001622", "A001654", "A001655", "A001656", "A001657", "A001658", "A084175", "A099930" ]
[ "M3989", "N1653" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001656.seq
b9524cb44b3d5f0259fcaf0d601eb9ee
A001657
Fibonomial coefficients: column 5 of A010048.
[ "1", "8", "104", "1092", "12376", "136136", "1514513", "16776144", "186135312", "2063912136", "22890661872", "253854868176", "2815321003313", "31222272414424", "346260798314872", "3840089017377228", "42587248616222024", "472299787252290712", "5237885063192296801", "580890348266...
[ "nonn", "easy" ]
85
0
2
[ "A000045", "A001076", "A001654", "A001657", "A001658", "A010048", "A049666", "A065563", "A079586" ]
[ "M4568", "N1945" ]
N. J. A. Sloane
2025-12-16T02:22:46
oeisdata/seq/A001/A001657.seq
ab80d7d70dc264c48ec45cc760bd54e3
A001658
Fibonomial coefficients.
[ "1", "13", "273", "4641", "85085", "1514513", "27261234", "488605194", "8771626578", "157373300370", "2824135408458", "50675778059634", "909348684070099", "16317540120588343", "292806787575013635", "5254201798026392211", "94282845030238533383", "1691836875411111866723", "30358781...
[ "nonn", "easy" ]
80
0
2
[ "A001654", "A001656", "A001657", "A001658" ]
[ "M4919", "N2112" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001658.seq
875a78410e9432950c4bed1e79396180
A001659
Expansion of bracket function.
[ "1", "1", "-1", "2", "-5", "13", "-33", "80", "-184", "402", "-840", "1699", "-3382", "6750", "-13716", "28550", "-60587", "129579", "-275915", "579828", "-1197649", "2431775", "-4870105", "9672634", "-19173013", "38151533", "-76521331", "154941608", "-3163992...
[ "sign" ]
42
1
4
[ "A000005", "A000748", "A000749", "A000750", "A001659", "A006090", "A006218", "A038200" ]
[ "M1433", "N0567" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001659.seq
8eae189faa02fee53c579d83aeed339a
A001660
Hypotenusal numbers.
[ "1", "1", "2", "6", "36", "876", "408696", "83762796636", "3508125906207095591916", "6153473687096578758445014683368786661634996", "18932619208894981833333582059033329370801260096062214926751788496235698477988081702676" ]
[ "nonn", "easy", "nice" ]
23
0
3
[ "A000905", "A001660" ]
[ "M1706", "N0675" ]
N. J. A. Sloane
2015-10-12T23:05:16
oeisdata/seq/A001/A001660.seq
c5dfcf7682661cecbfb93ad77c749397
A001661
Largest number not the sum of distinct positive n-th powers.
[ "128", "12758", "5134240", "67898771", "11146309947", "766834015734", "4968618780985762" ]
[ "nonn", "nice", "more", "hard" ]
103
2
1
[ "A001661", "A030052", "A121571", "A173563", "A279529" ]
[ "M5393", "N2342" ]
N. J. A. Sloane and Robert G. Wilson v
2025-02-16T08:32:24
oeisdata/seq/A001/A001661.seq
45e39d027dfd2f3a121c7be444296bdb
A001662
Coefficients of Airey's converging factor.
[ "0", "1", "1", "-1", "-1", "13", "-47", "-73", "2447", "-16811", "-15551", "1726511", "-18994849", "10979677", "2983409137", "-48421103257", "135002366063", "10125320047141", "-232033147779359", "1305952009204319", "58740282660173759", "-1862057132555380307", "16905219421...
[ "sign", "easy", "nice" ]
240
0
6
[ "A001662", "A032188", "A051711", "A274447", "A274448", "A340556" ]
[ "M4896", "N2098" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001662.seq
e32d8831b477829d8662f29d8b808223
A001663
Linear coefficient of the n-th converging polynomial of Weber functions (Erroneous version).
[ "1", "-3", "7", "-5", "-93", "637", "-1425", "-22341" ]
[ "sign" ]
38
1
2
[ "A001662", "A001663", "A001664", "A380170" ]
[ "M2610", "N1032" ]
N. J. A. Sloane
2025-01-14T09:58:24
oeisdata/seq/A001/A001663.seq
c1dcfb8e288efed9d272d3b88a668182
A001664
Quadratic coefficient of the n-th converging polynomial of Weber functions.
[ "1", "-6", "25", "-60", "-203", "3710", "-21347", "-50400", "2465969", "-24201342", "-14909791", "4154706556", "-61829802067", "107889525510", "13926895008805", "-296622934827816", "1387504872714793", "80367331405832714", "-2381736125794455767", "19480923855903871284", "72153...
[ "sign" ]
28
2
2
[ "A001662", "A001663", "A001664" ]
[ "M4165", "N1732" ]
N. J. A. Sloane
2025-01-13T15:19:08
oeisdata/seq/A001/A001664.seq
e0dfbfc366652d1624bc4c3188d7804e
A001665
Number of self-avoiding n-step walks on Kagome lattice.
[ "1", "4", "12", "32", "88", "240", "652", "1744", "4616", "12208", "32328", "85408", "224640", "589024", "1542944", "4039256", "10560552", "27567488", "71878068", "187262944", "487526944", "1268269160", "3296832292", "8564411120", "22235825104", "57701041072", "14...
[ "nonn", "walk", "nice" ]
20
0
2
null
[ "M3445", "N1399" ]
N. J. A. Sloane
2024-10-18T11:43:27
oeisdata/seq/A001/A001665.seq
92ceca1f0977079e3b4a17c29303fefe
A001666
Number of n-step self-avoiding walks on b.c.c. lattice (version 2).
[ "1", "8", "56", "392", "2648", "17960", "120056", "804824", "5351720", "35652680", "236291096", "1568049560", "10368669992", "68626647608", "453032542040", "2992783648424", "19731335857592", "130161040083608", "857282278813256", "5648892048530888", "37175039569217672", "244...
[ "nonn", "walk", "nice" ]
34
0
2
[ "A001336", "A001412", "A001666", "A002903" ]
[ "M4545", "N1929" ]
N. J. A. Sloane
2025-10-08T01:09:19
oeisdata/seq/A001/A001666.seq
b4a17c3e74d097c1b6c7ed6e7f6fe7c7
A001667
2n-step polygons on b.c.c. lattice.
[ "96", "1776", "43776", "1237920", "37903776", "1223681760", "41040797376", "1416762272736", "50027402384640", "1799035070369856" ]
[ "nonn", "nice", "walk", "more" ]
29
2
1
[ "A001337", "A001413", "A001666", "A001667", "A038515" ]
[ "M5364", "N2330" ]
N. J. A. Sloane
2025-10-07T19:30:07
oeisdata/seq/A001/A001667.seq
bc222cce2e584dc3abc18728ef0e645d
A001668
Number of self-avoiding n-step walks on honeycomb lattice.
[ "1", "3", "6", "12", "24", "48", "90", "174", "336", "648", "1218", "2328", "4416", "8388", "15780", "29892", "56268", "106200", "199350", "375504", "704304", "1323996", "2479692", "4654464", "8710212", "16328220", "30526374", "57161568", "106794084", "19978...
[ "nonn", "walk", "nice" ]
63
0
2
[ "A001668", "A006851" ]
[ "M2559", "N1013" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001668.seq
523f6c509a95b753f40a60b0529aeba1
A001669
Number of 7-level labeled rooted trees with n leaves.
[ "1", "1", "7", "70", "910", "14532", "274778", "5995892", "148154860", "4085619622", "124304629050", "4133867297490", "149114120602860", "5796433459664946", "241482353893283349", "10730629952953517859", "506500241174366575122", "25302666611855946733140" ]
[ "nonn", "easy" ]
46
0
3
[ "A000110", "A000258", "A000307", "A000357", "A000405", "A001669", "A144150" ]
[ "M4443", "N1879" ]
N. J. A. Sloane
2022-02-01T01:21:37
oeisdata/seq/A001/A001669.seq
1fd331f9d2c2a6c36be8ee6010ae42be
A001670
k appears k times (k even).
[ "2", "2", "4", "4", "4", "4", "6", "6", "6", "6", "6", "6", "8", "8", "8", "8", "8", "8", "8", "8", "10", "10", "10", "10", "10", "10", "10", "10", "10", "10", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", ...
[ "nonn", "easy" ]
48
1
1
[ "A000194", "A001650", "A001670", "A130829" ]
null
N. J. A. Sloane
2025-05-08T07:22:46
oeisdata/seq/A001/A001670.seq
de936edfc5020e8842788b26063e3e1a
A001671
Powers of e rounded up.
[ "1", "3", "8", "21", "55", "149", "404", "1097", "2981", "8104", "22027", "59875", "162755", "442414", "1202605", "3269018", "8886111", "24154953", "65659970", "178482301", "485165196", "1318815735", "3584912847", "9744803447", "26489122130", "72004899338", "19572...
[ "nonn" ]
17
0
2
[ "A000149", "A000227", "A001671" ]
null
N. J. A. Sloane
2018-05-28T15:35:59
oeisdata/seq/A001/A001671.seq
7f046dce020280f02ab7e3bf2b825ea0
A001672
a(n) = floor(Pi^n).
[ "1", "3", "9", "31", "97", "306", "961", "3020", "9488", "29809", "93648", "294204", "924269", "2903677", "9122171", "28658145", "90032220", "282844563", "888582403", "2791563949", "8769956796", "27551631842", "86556004191", "271923706893", "854273519913", "26837794...
[ "nonn" ]
23
0
2
[ "A001672", "A001673", "A002160" ]
null
N. J. A. Sloane
2018-05-28T14:22:40
oeisdata/seq/A001/A001672.seq
a791278775291ca2d81c59ab6b615ee2
A001673
a(n) = ceiling(Pi^n).
[ "1", "4", "10", "32", "98", "307", "962", "3021", "9489", "29810", "93649", "294205", "924270", "2903678", "9122172", "28658146", "90032221", "282844564", "888582404", "2791563950", "8769956797", "27551631843", "86556004192", "271923706894", "854273519914", "2683779...
[ "nonn" ]
12
0
2
null
null
N. J. A. Sloane
2016-12-19T01:20:59
oeisdata/seq/A001/A001673.seq
a01119909d89789ffc92ac7d66f36c0c
A001674
a(n) = floor(sqrt( 2*Pi )^n).
[ "1", "2", "6", "15", "39", "98", "248", "621", "1558", "3906", "9792", "24546", "61528", "154230", "386597", "969056", "2429063", "6088760", "15262258", "38256809", "95895600", "240374623", "602529828", "1510318305", "3785806567", "9489609784", "23786924200", "5...
[ "nonn" ]
11
0
2
[ "A000149", "A001672", "A001674", "A014217", "A017910", "A032739", "A062541", "A121831" ]
null
N. J. A. Sloane
2022-02-01T01:21:53
oeisdata/seq/A001/A001674.seq
cd90cf1078204cc766e85c95e734e3a9
A001675
a(n) = round(sqrt( 2*Pi )^n).
[ "1", "3", "6", "16", "39", "99", "248", "622", "1559", "3907", "9793", "24546", "61529", "154230", "386598", "969056", "2429064", "6088760", "15262259", "38256810", "95895601", "240374624", "602529829", "1510318305", "3785806568", "9489609784", "23786924201", "5...
[ "nonn" ]
16
0
2
[ "A000227", "A001674", "A001675", "A001698", "A002160", "A017911" ]
null
N. J. A. Sloane
2022-02-01T01:22:08
oeisdata/seq/A001/A001675.seq
42aeeaee42da35fb085c6ef29e596afc
A001676
Number of h-cobordism classes of smooth homotopy n-spheres.
[ "1", "1", "1", "1", "1", "1", "28", "2", "8", "6", "992", "1", "3", "2", "16256", "2", "16", "16", "523264", "24", "8", "4", "69524373504", "2", "4", "12", "67100672", "2", "3", "3", "7767211311104", "8", "32", "32", "3014494287036416", "6", "2...
[ "nonn", "hard", "nice" ]
103
1
7
[ "A001676", "A048648", "A053381", "A057617", "A187595", "A187717", "A189995", "A191783", "A228689", "A228690", "A228691", "A228692" ]
[ "M5197", "N2261" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001676.seq
d00b5d8431f8c1f57faa933ecfbaa1a0
A001677
Number of series-parallel networks with n edges.
[ "1", "2", "3", "6", "12", "26", "59", "146", "368", "976", "2667", "7482", "21440", "62622", "185637", "557680", "1694256", "5198142", "16086486", "50165218", "157510504", "497607008", "1580800091", "5047337994", "16190223624", "52153429218", "168657986843", "54...
[ "nonn", "nice", "easy" ]
32
2
2
[ "A001677", "A058642", "A058668" ]
[ "M0797", "N0302" ]
N. J. A. Sloane
2025-07-08T16:26:52
oeisdata/seq/A001/A001677.seq
6482b00736bfa1194b1c4dba0521a790
A001678
Number of series-reduced planted trees with n nodes.
[ "0", "0", "1", "0", "1", "1", "2", "3", "6", "10", "19", "35", "67", "127", "248", "482", "952", "1885", "3765", "7546", "15221", "30802", "62620", "127702", "261335", "536278", "1103600", "2276499", "4706985", "9752585", "20247033", "42110393", "87733...
[ "nonn", "easy", "nice" ]
103
0
7
[ "A000014", "A000081", "A000669", "A001678", "A001679", "A004111", "A005202", "A007827", "A060356", "A106179", "A108919", "A198518", "A246403", "A254382", "A291636", "A330951", "A331488", "A331578" ]
[ "M0768", "N0293" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001678.seq
2a321679cd426f69529ccbccc36ffbb7
A001679
Number of series-reduced rooted trees with n nodes.
[ "1", "1", "1", "0", "2", "2", "4", "6", "12", "20", "39", "71", "137", "261", "511", "995", "1974", "3915", "7841", "15749", "31835", "64540", "131453", "268498", "550324", "1130899", "2330381", "4813031", "9963288", "20665781", "42947715", "89410092", ...
[ "nonn" ]
62
0
5
[ "A000014", "A000055", "A000081", "A000669", "A001678", "A001679", "A004111", "A005512", "A059123", "A060313", "A060356", "A198518", "A246403", "A254382", "A291636", "A330951", "A331488", "A331489", "A331578" ]
[ "M0327", "N0123" ]
N. J. A. Sloane
2025-02-16T08:32:24
oeisdata/seq/A001/A001679.seq
e43e3b6d6987999701989d2615260691
A001680
The partition function G(n,3).
[ "1", "1", "2", "5", "14", "46", "166", "652", "2780", "12644", "61136", "312676", "1680592", "9467680", "55704104", "341185496", "2170853456", "14314313872", "97620050080", "687418278544", "4989946902176", "37286121988256", "286432845428192", "2259405263572480", "1828...
[ "nonn" ]
87
0
3
[ "A001680", "A001681", "A189886", "A229223" ]
[ "M1465", "N0579" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001680.seq
2f17f0cac1c7a85d75a10820f7bf32ac
A001681
The partition function G(n,4).
[ "1", "1", "2", "5", "15", "51", "196", "827", "3795", "18755", "99146", "556711", "3305017", "20655285", "135399720", "927973061", "6631556521", "49294051497", "380306658250", "3039453750685", "25120541332271", "214363100120051", "1885987611214092", "17085579637664715",...
[ "nonn", "easy" ]
75
0
3
[ "A001680", "A001681", "A229223", "A276924" ]
[ "M1481", "N0584" ]
N. J. A. Sloane
2025-11-05T15:21:40
oeisdata/seq/A001/A001681.seq
9d51d2a70c4e0bc523c286bdf94f2ab7
A001682
Numbers k such that 3^k, 3^(k+1) and 3^(k+2) have the same number of digits.
[ "0", "21", "42", "65", "86", "109", "130", "151", "174", "195", "218", "239", "262", "283", "304", "327", "348", "371", "392", "415", "436", "457", "480", "501", "524", "545", "568", "589", "610", "633", "654", "677", "698", "721", "742", "763", ...
[ "nonn", "base", "easy", "nice" ]
36
1
2
[ "A000244", "A001682", "A055642", "A151910" ]
[ "M5109", "N2213" ]
N. J. A. Sloane
2021-02-11T23:00:33
oeisdata/seq/A001/A001682.seq
f0b9dbf6e0b185f9d621885c57eed3b8
A001683
Number of one-sided triangulations of the disk; or flexagons of order n; or unlabeled plane trivalent trees (n-2 internal vertices, all of degree 3 and hence n leaves).
[ "1", "1", "1", "1", "4", "6", "19", "49", "150", "442", "1424", "4522", "14924", "49536", "167367", "570285", "1965058", "6823410", "23884366", "84155478", "298377508", "1063750740", "3811803164", "13722384546", "49611801980", "180072089896", "655977266884", "23...
[ "nonn", "nice", "easy" ]
128
2
5
[ "A000108", "A000131", "A000207", "A001683", "A005034", "A007173", "A007282", "A057162", "A208355", "A262586", "A295224", "A369314" ]
[ "M3288", "N1325" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001683.seq
b90a22bd33fbc629a4593cc79f86bade
A001684
From a continued fraction.
[ "1", "1", "1", "1", "2", "6", "30", "390", "32370", "81022110", "79098077953830", "2499603048957386233742790", "6399996109983215106481566902449146981585570", "1296147136591533261616288032775924136752630487513536584267056282299509616710" ]
[ "nonn" ]
27
0
5
null
[ "M1693", "N0669" ]
N. J. A. Sloane
2025-11-29T10:09:10
oeisdata/seq/A001/A001684.seq
a1a4167a8db58c02560f7bae06e0f557
A001685
a(0) = 1, a(1) = 2, a(2) = 3; for n >= 3, a(n) = a(n-2) + a(n-1)*Product_{i=1..n-3} a(i).
[ "1", "2", "3", "5", "13", "83", "2503", "976253", "31601312113", "2560404986164794683", "202523113189037952478722304798003", "506227391211661106785411233681995783881012463859772443053" ]
[ "nonn" ]
45
0
2
[ "A001685", "A003686", "A064526", "A109134" ]
[ "M0740", "N0278" ]
N. J. A. Sloane
2025-11-29T10:09:18
oeisdata/seq/A001/A001685.seq
1ae4af8a58279698769da58fac83d796
A001686
From a continued fraction.
[ "1", "1", "2", "3", "8", "51", "1538", "599871", "19417825808", "1573273218577214751", "124442887685693556895657990772138", "311057821480221188367831306672353513246409033360367599771" ]
[ "nonn" ]
27
0
3
[ "A001684", "A001685", "A001686" ]
[ "M0893", "N0338" ]
N. J. A. Sloane
2025-11-29T10:09:04
oeisdata/seq/A001/A001686.seq
0e127e755558eb72a605dc0a5cd67faf
A001687
a(n) = a(n-2) + a(n-5).
[ "0", "1", "0", "1", "0", "1", "1", "1", "2", "1", "3", "2", "4", "4", "5", "7", "7", "11", "11", "16", "18", "23", "29", "34", "45", "52", "68", "81", "102", "126", "154", "194", "235", "296", "361", "450", "555", "685", "851", "1046", ...
[ "nonn" ]
64
0
9
[ "A001687", "A005686" ]
[ "M0147", "N0059" ]
N. J. A. Sloane, following a suggestion from Robert G. Wilson v
2025-11-05T15:35:23
oeisdata/seq/A001/A001687.seq
7b1c6eae512c1d2e5f6c53b1dd9f2318
A001688
4th forward differences of factorial numbers A000142.
[ "9", "53", "362", "2790", "24024", "229080", "2399760", "27422640", "339696000", "4536362880", "64988179200", "994447238400", "16190733081600", "279499828608000", "5100017213491200", "98087346669312000", "1983334021853184000", "42063950934061056000", "933754193111900160000" ]
[ "nonn", "easy" ]
48
0
1
[ "A000142", "A001563", "A001564", "A001565", "A001688", "A001689", "A095177" ]
[ "M4636", "N1980" ]
N. J. A. Sloane
2021-07-27T21:20:05
oeisdata/seq/A001/A001688.seq
e4ba7752d6c8fbeddf991f034de4686c
A001689
5th forward differences of factorial numbers A000142.
[ "44", "309", "2428", "21234", "205056", "2170680", "25022880", "312273360", "4196666880", "60451816320", "929459059200", "15196285843200", "263309095526400", "4820517384883200", "92987329455820800", "1885246675183872000", "40080616912207872000", "891690242177839104000" ]
[ "nonn", "easy" ]
43
0
1
[ "A000142", "A001563", "A001564", "A001565", "A001688", "A001689", "A096307" ]
[ "M4531", "N1920" ]
N. J. A. Sloane
2021-07-27T04:03:14
oeisdata/seq/A001/A001689.seq
a29561045450522a808b8b2515d47b5f
A001690
Non-Fibonacci numbers.
[ "4", "6", "7", "9", "10", "11", "12", "14", "15", "16", "17", "18", "19", "20", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", ...
[ "nonn", "easy", "nice" ]
94
1
1
[ "A000045", "A001690", "A010056" ]
[ "M3268", "N1319" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001690.seq
0a2916df254740c8328383b49dd1c87f
A001691
Number of two-element generating sets in the symmetric group S_n.
[ "0", "1", "9", "108", "3420", "114480", "7786800", "497266560", "42616445760", "4320959126400", "534444478444800", "77699101730342400", "13282131639801024000" ]
[ "nonn", "more" ]
35
1
3
[ "A001691", "A071605", "A086373" ]
[ "M4660", "N1995" ]
N. J. A. Sloane
2022-02-01T07:12:34
oeisdata/seq/A001/A001691.seq
7ba0999a1740ff1b6327d6169249e59d
A001692
Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras.
[ "1", "5", "10", "40", "150", "624", "2580", "11160", "48750", "217000", "976248", "4438920", "20343700", "93900240", "435959820", "2034504992", "9536718750", "44878791360", "211927516500", "1003867701480", "4768371093720", "22706531339280" ]
[ "nonn", "nice", "easy" ]
78
0
2
[ "A000351", "A001037", "A001692", "A002105", "A008683", "A027750", "A054720", "A074650" ]
[ "M3804", "N1554" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001692.seq
4a669f88d6cb21f34599a8bd8112229b
A001693
Number of degree-n irreducible polynomials over GF(7); dimensions of free Lie algebras.
[ "1", "7", "21", "112", "588", "3360", "19544", "117648", "720300", "4483696", "28245840", "179756976", "1153430600", "7453000800", "48444446376", "316504099520", "2077057800300", "13684147881600", "90467419857752", "599941851861744" ]
[ "nonn", "easy", "nice" ]
53
0
2
[ "A000031", "A001037", "A001693", "A027376", "A032164", "A074650" ]
[ "M4373", "N1838" ]
N. J. A. Sloane
2025-11-05T15:35:23
oeisdata/seq/A001/A001693.seq
846596c035dadd776bfb35914e82902f
A001694
Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).
[ "1", "4", "8", "9", "16", "25", "27", "32", "36", "49", "64", "72", "81", "100", "108", "121", "125", "128", "144", "169", "196", "200", "216", "225", "243", "256", "288", "289", "324", "343", "361", "392", "400", "432", "441", "484", "500", ...
[ "nonn", "nice", "easy" ]
235
1
2
[ "A001248", "A001694", "A003321", "A005188", "A005934", "A007532", "A013929", "A014576", "A023052", "A046074", "A052485", "A062503", "A076446", "A076871", "A112526", "A168363", "A224866", "A258599", "A261883", "A300717", "A320966", "A376361", "A376362" ]
[ "M3325", "N1335" ]
N. J. A. Sloane
2025-12-23T13:04:21
oeisdata/seq/A001/A001694.seq
eafe63df49d96c5f6bec00bbf8154b95
A001695
a(n) = H_n(2,n) where H_n is the n-th hyperoperator.
[ "1", "3", "4", "8", "65536" ]
[ "nonn", "nice" ]
63
0
2
[ "A001695", "A014221", "A046859", "A054871" ]
[ "M2352", "N0929" ]
N. J. A. Sloane, following a suggestion from Robert G. Wilson v, Aug 31 1994
2025-11-05T15:35:23
oeisdata/seq/A001/A001695.seq
db7f4c12290825aef8d99d523f019ec9
A001696
a(n) = a(n-1)*(1 + a(n-1) - a(n-2)), a(0) = 0, a(1) = 1.
[ "0", "1", "2", "4", "12", "108", "10476", "108625644", "11798392680793836", "139202068568601568785946949658348", "19377215893777651167043206536157529523359277782016064519251404524" ]
[ "nonn", "easy" ]
49
0
3
[ "A001696", "A001697", "A039941" ]
[ "M1268", "N0487" ]
N. J. A. Sloane
2025-11-26T15:59:31
oeisdata/seq/A001/A001696.seq
1375eada2001b88025140bccd6210785
A001697
a(n+1) = a(n)(a(0) + ... + a(n)).
[ "1", "1", "2", "8", "96", "10368", "108615168", "11798392572168192", "139202068568601556987554268864512", "19377215893777651167043206536157390321290709180447278572301746176" ]
[ "nonn", "easy", "nice", "changed" ]
68
0
3
[ "A001696", "A001697", "A001699", "A002658", "A039941", "A064847" ]
[ "M1902", "N0751" ]
N. J. A. Sloane
2026-01-10T07:31:54
oeisdata/seq/A001/A001697.seq
9c51912cba60d31ffae76fb83b114f39
A001698
a(n) = ceiling(sqrt( 2*Pi )^n).
[ "1", "3", "7", "16", "40", "99", "249", "622", "1559", "3907", "9793", "24547", "61529", "154231", "386598", "969057", "2429064", "6088761", "15262259", "38256810", "95895601", "240374624", "602529829", "1510318306", "3785806568", "9489609785", "23786924201", "5...
[ "nonn" ]
16
0
2
null
null
N. J. A. Sloane
2016-12-19T01:21:32
oeisdata/seq/A001/A001698.seq
870999c726da199d020efd1f7327379a
A001699
Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative.
[ "1", "1", "3", "21", "651", "457653", "210065930571", "44127887745696109598901", "1947270476915296449559659317606103024276803403", "3791862310265926082868235028027893277370233150300118107846437701158064808916492244872560821" ]
[ "nonn", "easy", "core", "nice" ]
122
0
3
[ "A001699", "A002449", "A002658", "A003095", "A004019", "A056207", "A065329", "A076949", "A077496", "A213437", "A335919", "A335920" ]
[ "M3087", "N1251" ]
N. J. A. Sloane and Jeffrey Shallit
2025-11-26T15:59:31
oeisdata/seq/A001/A001699.seq
f9a3d7dd45432c2acd115b39a81e4308
A001700
a(n) = binomial(2*n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.
[ "1", "3", "10", "35", "126", "462", "1716", "6435", "24310", "92378", "352716", "1352078", "5200300", "20058300", "77558760", "300540195", "1166803110", "4537567650", "17672631900", "68923264410", "269128937220", "1052049481860", "4116715363800", "16123801841550", "63...
[ "easy", "nonn", "nice", "core" ]
713
0
2
[ "A000108", "A000110", "A000984", "A001263", "A001405", "A001448", "A001700", "A001792", "A001813", "A002054", "A002458", "A005043", "A005773", "A007318", "A028364", "A030662", "A035324", "A039598", "A046097", "A049027", "A050166", "A060150", "A060897", "A060900", "A07...
[ "M2848", "N1144" ]
N. J. A. Sloane
2025-11-22T16:36:53
oeisdata/seq/A001/A001700.seq
bf240a37c0462c87c78d4bd8866d810d