A035443 Number of partitions of n into parts 8k or 8k+3.

0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 2, 1, 2, 2, 1, 4, 2, 1, 5, 2, 4, 5, 2, 8, 5, 2, 10, 5, 7, 11, 5, 14, 11, 5, 19, 11, 12, 21, 11, 24, 22, 11, 33, 22, 22, 38, 22, 41, 40, 22, 58, 41, 37, 68, 41, 67, 73, 41, 95, 75, 63, 114, 76, 108, 124, 76, 155, 129, 106, 188, 131, 173

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

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

Crossrefs

Cf. A035674.

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+3))), {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 + 3}];
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(3/8) / (4 * 2^(3/16) * 3^(7/16) * Pi^(5/8) * n^(15/16)). - Vaclav Kotesovec, Aug 26 2015