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

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

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

Crossrefs

Cf. A035679.

Programs

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 *)

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