A035458 - OEIS

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A035458

Number of partitions of n into parts 8k+2 or 8k+7.

0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 3, 4, 3, 5, 4, 6, 5, 7, 7, 8, 8, 10, 9, 13, 11, 15, 14, 17, 17, 20, 20, 24, 23, 29, 28, 33, 33, 38, 39, 45, 45, 53, 53, 61, 62, 70, 72, 81, 83, 95, 96, 108, 111, 124, 128, 142, 147, 164, 168, 187, 193, 212, 221, 242, 252, 277

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OFFSET

1,10

LINKS

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

FORMULA

a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(7/8) * Gamma(1/4) / (4 * 2^(9/16) * 3^(5/16) * Pi^(7/8) * n^(13/16)). - Vaclav Kotesovec, Aug 26 2015

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+7))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)

nmax = 60; kmax = nmax/8;

s = Flatten[{Range[0, kmax]*8 + 2}~Join~{Range[0, kmax]*8 + 7}];

Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 04 2020 *)

CROSSREFS

Sequence in context: A271315 A212813 A112219 * A259771 A357457 A194902

Adjacent sequences: A035455 A035456 A035457 * A035459 A035460 A035461

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved