A035447 - OEIS

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A035447

Number of partitions of n into parts 8k or 8k+7.

0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 2, 4, 3, 0, 0, 0, 1, 2, 5, 7, 5, 0, 0, 1, 2, 5, 9, 12, 7, 0, 1, 2, 5, 10, 17, 19, 11, 1, 2, 5, 10, 19, 28, 30, 16, 2, 5, 10, 20, 33, 47, 46, 24, 5, 10, 20, 35, 57, 74, 69, 35, 10, 20, 36, 62, 93, 116, 102, 52, 20, 36, 64

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OFFSET

1,15

LINKS

Robert Price, Table of n, a(n) for n = 1..1000

FORMULA

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(7/8) / (2^(23/16) * 3^(11/16) * Pi^(1/8) * n^(19/16)). - Vaclav Kotesovec, Aug 26 2015

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+7))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)

nmax = 50; kmax = nmax/8;

s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 7}];

Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)

CROSSREFS

Cf. A035679.

Sequence in context: A027359 A236109 A279279 * A227188 A354107 A037863

Adjacent sequences: A035444 A035445 A035446 * A035448 A035449 A035450

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved