Datasets:
RenaudGaudron
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oeis-sequences-benchmark

Dataset card Data Studio Files
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1
sequence_id
string
sequence_name
string
sequence_first_terms
list
sequence_next_term
string
is_easy
int64
A000001
Number of groups of order n.
[ "0", "1", "1", "1", "2", "1", "2", "1", "5", "2", "2", "1", "5", "1", "2", "1", "14", "1", "5" ]
1
0
A000002
Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's.
[ "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "1", "2", "2" ]
1
1
A000003
Number of classes of primitive positive definite binary quadratic forms of discriminant D = -4n; or equivalently the class number of the quadratic order of discriminant D = -4n.
[ "1", "1", "1", "1", "2", "2", "1", "2", "2", "2", "3", "2", "2", "4", "2", "2", "4", "2", "3" ]
4
1
A000004
The zero sequence.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
0
1
A000005
d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.
[ "1", "2", "2", "3", "2", "4", "2", "4", "3", "4", "2", "6", "2", "4", "4", "5", "2", "6", "2" ]
6
1
A000006
Integer part of square root of n-th prime.
[ "1", "1", "2", "2", "3", "3", "4", "4", "4", "5", "5", "6", "6", "6", "6", "7", "7", "7", "8" ]
8
1
A000007
The characteristic function of {0}: a(n) = 0^n.
[ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
0
1
A000008
Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.
[ "1", "1", "2", "2", "3", "4", "5", "6", "7", "8", "11", "12", "15", "16", "19", "22", "25", "28", "31" ]
34
1
A000009
Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.
[ "1", "1", "1", "2", "2", "3", "4", "5", "6", "8", "10", "12", "15", "18", "22", "27", "32", "38", "46" ]
54
1
A000010
Euler totient function phi(n): count numbers <= n and prime to n.
[ "1", "1", "2", "2", "4", "2", "6", "4", "6", "4", "10", "4", "12", "6", "8", "8", "16", "6", "18" ]
8
1
A000011
Number of n-bead necklaces (turning over is allowed) where complements are equivalent.
[ "1", "1", "2", "2", "4", "4", "8", "9", "18", "23", "44", "63", "122", "190", "362", "612", "1162", "2056", "3914" ]
7155
1
A000012
The simplest sequence of positive numbers: the all 1's sequence.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
1
1
A000013
Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed.
[ "1", "1", "2", "2", "4", "4", "8", "10", "20", "30", "56", "94", "180", "316", "596", "1096", "2068", "3856", "7316" ]
13798
1
A000014
Number of series-reduced trees with n nodes.
[ "0", "1", "1", "0", "1", "1", "2", "2", "4", "5", "10", "14", "26", "42", "78", "132", "249", "445", "842" ]
1561
1
A000015
Smallest prime power >= n.
[ "1", "2", "3", "4", "5", "7", "7", "8", "9", "11", "11", "13", "13", "16", "16", "16", "17", "19", "19" ]
23
1
A000016
a(n) is the number of distinct (infinite) output sequences from binary n-stage shift register which feeds back the complement of the last stage.
[ "1", "1", "1", "2", "2", "4", "6", "10", "16", "30", "52", "94", "172", "316", "586", "1096", "2048", "3856", "7286" ]
13798
1
A000017
Erroneous version of A032522.
[ "1", "0", "0", "2", "2", "4", "8", "4", "16", "12", "48", "80", "136", "420", "1240", "2872", "7652", "18104" ]
50184
0
A000018
Number of positive integers <= 2^n of form x^2 + 16*y^2.
[ "1", "1", "2", "2", "4", "8", "13", "25", "44", "83", "152", "286", "538", "1020", "1942", "3725", "7145", "13781", "26627" ]
51572
0
A000019
Number of primitive permutation groups of degree n.
[ "1", "1", "2", "2", "5", "4", "7", "7", "11", "9", "8", "6", "9", "4", "6", "22", "10", "4", "8" ]
4
0
A000020
Number of primitive polynomials of degree n over GF(2) (version 2).
[ "2", "1", "2", "2", "6", "6", "18", "16", "48", "60", "176", "144", "630", "756", "1800", "2048", "7710", "7776", "27594" ]
24000
0
A000021
Number of positive integers <= 2^n of form x^2 + 12 y^2.
[ "1", "1", "2", "2", "6", "9", "17", "30", "54", "98", "183", "341", "645", "1220", "2327", "4451", "8555", "16489", "31859" ]
61717
0
A000022
Number of centered hydrocarbons with n atoms.
[ "0", "1", "0", "1", "1", "2", "2", "6", "9", "20", "37", "86", "181", "422", "943", "2223", "5225", "12613", "30513" ]
74883
1
A000023
Expansion of e.g.f. exp(-2*x)/(1-x).
[ "1", "-1", "2", "-2", "8", "8", "112", "656", "5504", "49024", "491264", "5401856", "64826368", "842734592", "11798300672", "176974477312", "2831591702528", "48137058811904", "866467058876416" ]
16462874118127616
1
A000024
Number of positive integers <= 2^n of form x^2 + 10 y^2.
[ "1", "1", "2", "2", "7", "10", "20", "36", "65", "118", "221", "409", "776", "1463", "2788", "5328", "10222", "19714", "38054" ]
73685
0
A000025
Coefficients of the 3rd-order mock theta function f(q).
[ "1", "1", "-2", "3", "-3", "3", "-5", "7", "-6", "6", "-10", "12", "-11", "13", "-17", "20", "-21", "21", "-27" ]
34
1
A000026
Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).
[ "1", "2", "3", "4", "5", "6", "7", "6", "6", "10", "11", "12", "13", "14", "15", "8", "17", "12", "19" ]
20
1
A000027
The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19" ]
20
1
A000028
Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.
[ "2", "3", "4", "5", "7", "9", "11", "13", "16", "17", "19", "23", "24", "25", "29", "30", "31", "37", "40" ]
41
1
A000029
Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).
[ "1", "2", "3", "4", "6", "8", "13", "18", "30", "46", "78", "126", "224", "380", "687", "1224", "2250", "4112", "7685" ]
14310
1
A000030
Initial digit of n.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
1
1
A000031
Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.
[ "1", "2", "3", "4", "6", "8", "14", "20", "36", "60", "108", "188", "352", "632", "1182", "2192", "4116", "7712", "14602" ]
27596
1
A000032
Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1.
[ "2", "1", "3", "4", "7", "11", "18", "29", "47", "76", "123", "199", "322", "521", "843", "1364", "2207", "3571", "5778" ]
9349
1
A000033
Coefficients of ménage hit polynomials.
[ "0", "2", "3", "4", "40", "210", "1477", "11672", "104256", "1036050", "11338855", "135494844", "1755206648", "24498813794", "366526605705", "5851140525680", "99271367764480", "1783734385752162", "33837677493828171" ]
675799125332580020
1
A000034
Period 2: repeat [1, 2]; a(n) = 1 + (n mod 2).
[ "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1" ]
2
1
A000035
Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.
[ "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0" ]
1
1
A000036
Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives closest integer to P(A000099(n)).
[ "2", "3", "5", "6", "6", "-6", "7", "8", "10", "13", "13", "13", "14", "-17", "17", "17", "18", "-19", "20" ]
-22
0
A000037
Numbers that are not squares (or, the nonsquares).
[ "2", "3", "5", "6", "7", "8", "10", "11", "12", "13", "14", "15", "17", "18", "19", "20", "21", "22", "23" ]
24
1
A000038
Twice A000007.
[ "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
0
1
A000039
Coefficient of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
[ "1", "-2", "-3", "-5", "-6", "-10", "-11", "-17", "-21", "-27", "-33", "-46", "-53", "-68", "-82", "-104", "-123", "-154", "-179" ]
-221
0
A000040
The prime numbers.
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "29", "31", "37", "41", "43", "47", "53", "59", "61", "67" ]
71
1
A000041
a(n) is the number of partitions of n (the partition numbers).
[ "1", "1", "2", "3", "5", "7", "11", "15", "22", "30", "42", "56", "77", "101", "135", "176", "231", "297", "385" ]
490
1
A000042
Unary representation of natural numbers.
[ "1", "11", "111", "1111", "11111", "111111", "1111111", "11111111", "111111111", "1111111111", "11111111111", "111111111111", "1111111111111", "11111111111111", "111111111111111", "1111111111111111", "11111111111111111", "111111111111111111", "1111111111111111111" ]
11111111111111111111
1
A000043
Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.
[ "2", "3", "5", "7", "13", "17", "19", "31", "61", "89", "107", "127", "521", "607", "1279", "2203", "2281", "3217", "4253" ]
4423
0
A000044
Dying rabbits: a(0) = 1; for 1 <= n <= 12, a(n) = Fibonacci(n); for n >= 13, a(n) = a(n-1) + a(n-2) - a(n-13).
[ "1", "1", "1", "2", "3", "5", "8", "13", "21", "34", "55", "89", "144", "232", "375", "606", "979", "1582", "2556" ]
4130
1
A000045
Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
[ "0", "1", "1", "2", "3", "5", "8", "13", "21", "34", "55", "89", "144", "233", "377", "610", "987", "1597", "2584" ]
4181
1
A000046
Number of primitive n-bead necklaces (turning over is allowed) where complements are equivalent.
[ "1", "1", "1", "1", "2", "3", "5", "8", "14", "21", "39", "62", "112", "189", "352", "607", "1144", "2055", "3885" ]
7154
1
A000047
Number of integers <= 2^n of form x^2 - 2y^2.
[ "1", "2", "3", "5", "8", "15", "26", "48", "87", "161", "299", "563", "1066", "2030", "3885", "7464", "14384", "27779", "53782" ]
104359
0
A000048
Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.
[ "1", "1", "1", "1", "2", "3", "5", "9", "16", "28", "51", "93", "170", "315", "585", "1091", "2048", "3855", "7280" ]
13797
1
A000049
Number of positive integers <= 2^n of the form 3*x^2 + 4*y^2.
[ "0", "0", "2", "3", "5", "9", "16", "29", "53", "98", "181", "341", "640", "1218", "2321", "4449", "8546", "16482", "31845" ]
61707
0
A000050
Number of positive integers <= 2^n of form x^2 + y^2.
[ "1", "2", "3", "5", "9", "16", "29", "54", "97", "180", "337", "633", "1197", "2280", "4357", "8363", "16096", "31064", "60108" ]
116555
0
A000051
a(n) = 2^n + 1.
[ "2", "3", "5", "9", "17", "33", "65", "129", "257", "513", "1025", "2049", "4097", "8193", "16385", "32769", "65537", "131073", "262145" ]
524289
1
A000052
1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.
[ "8", "5", "4", "9", "1", "7", "6", "3", "2", "0", "18", "80", "88", "85", "84", "89", "81", "87", "86" ]
83
0
A000053
Local stops on New York City 1 Train (Broadway-7 Avenue Local) subway.
[ "14", "18", "23", "28", "34", "42", "50", "59", "66", "72", "79", "86", "96", "103", "110", "116", "125", "137", "145" ]
157
0
A000054
Local stops on New York City A line subway.
[ "4", "14", "23", "34", "42", "50", "59", "72", "81", "86", "96", "103", "110", "116", "125", "135", "145", "155", "163" ]
168
0
A000055
Number of trees with n unlabeled nodes.
[ "1", "1", "1", "1", "2", "3", "6", "11", "23", "47", "106", "235", "551", "1301", "3159", "7741", "19320", "48629", "123867" ]
317955
1
A000056
Order of the group SL(2,Z_n).
[ "1", "6", "24", "48", "120", "144", "336", "384", "648", "720", "1320", "1152", "2184", "2016", "2880", "3072", "4896", "3888", "6840" ]
5760
1
A000057
Primes dividing all Fibonacci sequences.
[ "2", "3", "7", "23", "43", "67", "83", "103", "127", "163", "167", "223", "227", "283", "367", "383", "443", "463", "467" ]
487
0
A000058
Sylvester's sequence: a(n+1) = a(n)^2 - a(n) + 1, with a(0) = 2.
[ "2", "3", "7", "43", "1807", "3263443", "10650056950807", "113423713055421844361000443" ]
12864938683278671740537145998360961546653259485195807
0
A000059
Numbers k such that (2k)^4 + 1 is prime.
[ "1", "2", "3", "8", "10", "12", "14", "17", "23", "24", "27", "28", "37", "40", "41", "44", "45", "53", "59" ]
66
1
A000060
Number of signed trees with n nodes.
[ "1", "2", "3", "10", "27", "98", "350", "1402", "5743", "24742", "108968", "492638", "2266502", "10600510", "50235931", "240882152", "1166732814", "5702046382", "28088787314" ]
139355139206
0
A000061
Generalized tangent numbers d(n,1).
[ "1", "1", "2", "4", "4", "6", "8", "8", "12", "14", "14", "16", "20", "20", "24", "32", "24", "30", "38" ]
32
0
A000062
A Beatty sequence: a(n) = floor(n/(e-2)).
[ "1", "2", "4", "5", "6", "8", "9", "11", "12", "13", "15", "16", "18", "19", "20", "22", "23", "25", "26" ]
27
0
A000063
Symmetrical dissections of an n-gon.
[ "1", "1", "2", "4", "5", "14", "14", "39", "42", "132", "132", "424", "429", "1428", "1430", "4848", "4862", "16796", "16796" ]
58739
0
A000064
Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents.
[ "1", "2", "4", "6", "9", "13", "18", "24", "31", "39", "50", "62", "77", "93", "112", "134", "159", "187", "218" ]
252
1
A000065
-1 + number of partitions of n.
[ "0", "0", "1", "2", "4", "6", "10", "14", "21", "29", "41", "55", "76", "100", "134", "175", "230", "296", "384" ]
489
1
A000066
Smallest number of vertices in trivalent graph with girth (shortest cycle) = n.
[ "4", "6", "10", "14", "24", "30", "58", "70", "112" ]
126
0
A000067
Number of positive integers <= 2^n of form x^2 + 2 y^2.
[ "1", "2", "4", "6", "10", "18", "33", "60", "111", "205", "385", "725", "1374", "2610", "4993", "9578", "18426", "35568", "68806" ]
133411
0
A000068
Numbers k such that k^4 + 1 is prime.
[ "1", "2", "4", "6", "16", "20", "24", "28", "34", "46", "48", "54", "56", "74", "80", "82", "88", "90", "106" ]
118
1
A000069
Odious numbers: numbers with an odd number of 1's in their binary expansion.
[ "1", "2", "4", "7", "8", "11", "13", "14", "16", "19", "21", "22", "25", "26", "28", "31", "32", "35", "37" ]
38
1
A000070
a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).
[ "1", "2", "4", "7", "12", "19", "30", "45", "67", "97", "139", "195", "272", "373", "508", "684", "915", "1212", "1597" ]
2087
1
A000071
a(n) = Fibonacci(n) - 1.
[ "0", "0", "1", "2", "4", "7", "12", "20", "33", "54", "88", "143", "232", "376", "609", "986", "1596", "2583", "4180" ]
6764
1
A000072
Number of positive integers <= 2^n of form x^2 + 4 y^2.
[ "1", "1", "2", "4", "7", "12", "22", "41", "72", "137", "254", "476", "901", "1716", "3274", "6286", "12090", "23331", "45140" ]
87511
0
A000073
Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3 with a(0) = a(1) = 0 and a(2) = 1.
[ "0", "0", "1", "1", "2", "4", "7", "13", "24", "44", "81", "149", "274", "504", "927", "1705", "3136", "5768", "10609" ]
19513
1
A000074
Number of odd integers <= 2^n of form x^2 + y^2.
[ "1", "1", "2", "4", "7", "13", "25", "43", "83", "157", "296", "564", "1083", "2077", "4006", "7733", "14968", "29044", "56447" ]
109864
0
A000075
Number of positive integers <= 2^n of form 2 x^2 + 3 y^2.
[ "0", "1", "2", "4", "7", "14", "23", "42", "76", "139", "258", "482", "907", "1717", "3269", "6257", "12020", "23171", "44762" ]
86683
0
A000076
Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.
[ "0", "0", "1", "2", "4", "7", "14", "24", "43", "82", "149", "284", "534", "1015", "1937", "3713", "7136", "13759", "26597" ]
51537
0
A000077
Number of positive integers <= 2^n of form x^2 + 6 y^2.
[ "1", "1", "2", "4", "8", "13", "24", "42", "76", "140", "257", "483", "907", "1717", "3272", "6261", "12027", "23172", "44769" ]
86708
0
A000078
Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) for n >= 4 with a(0) = a(1) = a(2) = 0 and a(3) = 1.
[ "0", "0", "0", "1", "1", "2", "4", "8", "15", "29", "56", "108", "208", "401", "773", "1490", "2872", "5536", "10671" ]
20569
1
A000079
Powers of 2: a(n) = 2^n.
[ "1", "2", "4", "8", "16", "32", "64", "128", "256", "512", "1024", "2048", "4096", "8192", "16384", "32768", "65536", "131072", "262144" ]
524288
1
A000080
Number of nonisomorphic minimal triangle graphs.
[ "1", "1", "2", "4", "9", "19", "48", "117", "307", "821", "2277", "6437", "18634", "54775", "163703", "495529", "1518706", "4703848", "14714754" ]
46444979
0
A000081
Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point).
[ "0", "1", "1", "2", "4", "9", "20", "48", "115", "286", "719", "1842", "4766", "12486", "32973", "87811", "235381", "634847", "1721159" ]
4688676
1
A000082
a(n) = n^2*Product_{p|n} (1 + 1/p).
[ "1", "6", "12", "24", "30", "72", "56", "96", "108", "180", "132", "288", "182", "336", "360", "384", "306", "648", "380" ]
720
1
A000083
Number of mixed Husimi trees with n nodes; or polygonal cacti with bridges.
[ "1", "1", "1", "2", "4", "9", "23", "63", "188", "596", "1979", "6804", "24118", "87379", "322652", "1209808", "4596158", "17657037", "68497898" ]
268006183
0
A000084
Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon.
[ "1", "2", "4", "10", "24", "66", "180", "522", "1532", "4624", "14136", "43930", "137908", "437502", "1399068", "4507352", "14611576", "47633486", "156047204" ]
513477502
1
A000085
Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.
[ "1", "1", "2", "4", "10", "26", "76", "232", "764", "2620", "9496", "35696", "140152", "568504", "2390480", "10349536", "46206736", "211799312", "997313824" ]
4809701440
1
A000086
Number of solutions to x^2 - x + 1 == 0 (mod n).
[ "1", "0", "1", "0", "0", "0", "2", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "2" ]
0
1
A000087
Number of unrooted nonseparable planar maps with n edges and a distinguished face.
[ "2", "1", "2", "4", "10", "37", "138", "628", "2972", "14903", "76994", "409594", "2222628", "12281570", "68864086", "391120036", "2246122574", "13025721601", "76194378042" ]
449155863868
0
A000088
Number of simple graphs on n unlabeled nodes.
[ "1", "1", "2", "4", "11", "34", "156", "1044", "12346", "274668", "12005168", "1018997864", "165091172592", "50502031367952", "29054155657235488", "31426485969804308768", "64001015704527557894928", "245935864153532932683719776", "1787577725145611700547878190848" ]
24637809253125004524383007491432768
0
A000089
Number of solutions to x^2 + 1 == 0 (mod n).
[ "1", "1", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "2", "0", "0", "0", "2", "0", "0" ]
0
0
A000090
Expansion of e.g.f. exp((-x^3)/3)/(1-x).
[ "1", "1", "2", "4", "16", "80", "520", "3640", "29120", "259840", "2598400", "28582400", "343235200", "4462057600", "62468806400", "936987251200", "14991796019200", "254860532326400", "4587501779660800" ]
87162533813555200
1
A000091
Multiplicative with a(2^e) = 2 for k >= 1; a(3) = 2, a(3^e) = 0 for k >= 2; a(p^e) = 0 if p > 3 and p == -1 (mod 3); a(p^e) = 2 if p > 3 and p == 1 (mod 3).
[ "1", "2", "2", "2", "0", "4", "2", "2", "0", "0", "0", "4", "2", "4", "0", "2", "0", "0", "2" ]
0
1
A000092
Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.
[ "1", "2", "5", "6", "14", "21", "29", "30", "54", "90", "134", "155", "174", "230", "234", "251", "270", "342", "374" ]
461
0
A000093
a(n) = floor(n^(3/2)).
[ "0", "1", "2", "5", "8", "11", "14", "18", "22", "27", "31", "36", "41", "46", "52", "58", "64", "70", "76" ]
82
1
A000094
Number of trees of diameter 4.
[ "0", "0", "0", "0", "1", "2", "5", "8", "14", "21", "32", "45", "65", "88", "121", "161", "215", "280", "367" ]
471
0
A000095
Number of fixed points of GAMMA_0 (n) of type i.
[ "1", "2", "0", "0", "2", "0", "0", "0", "0", "4", "0", "0", "2", "0", "0", "0", "2", "0", "0" ]
0
1
A000096
a(n) = n*(n+3)/2.
[ "0", "2", "5", "9", "14", "20", "27", "35", "44", "54", "65", "77", "90", "104", "119", "135", "152", "170", "189" ]
209
1
A000097
Number of partitions of n if there are two kinds of 1's and two kinds of 2's.
[ "1", "2", "5", "9", "17", "28", "47", "73", "114", "170", "253", "365", "525", "738", "1033", "1422", "1948", "2634", "3545" ]
4721
1
A000098
Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3.
[ "1", "2", "5", "10", "19", "33", "57", "92", "147", "227", "345", "512", "752", "1083", "1545", "2174", "3031", "4179", "5719" ]
7752
1
A000099
Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record.
[ "1", "2", "5", "10", "20", "24", "26", "41", "53", "130", "149", "205", "234", "287", "340", "410", "425", "480", "586" ]
840
0
A000100
a(n) is the number of compositions of n in which the maximal part is 3.
[ "0", "0", "0", "1", "2", "5", "11", "23", "47", "94", "185", "360", "694", "1328", "2526", "4781", "9012", "16929", "31709" ]
59247
1