A035364 Number of partitions of n into parts 4k or 4k+3.

0, 0, 1, 1, 0, 1, 2, 2, 1, 2, 4, 4, 2, 5, 8, 7, 5, 10, 14, 12, 11, 19, 24, 22, 21, 33, 41, 37, 38, 58, 67, 62, 68, 95, 108, 103, 114, 155, 172, 166, 188, 246, 268, 264, 303, 384, 413, 415, 477, 588, 630, 640, 737, 893, 948, 975, 1125, 1333, 1412, 1470, 1688

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(4k+4))*(1 - x^(4k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ exp(Pi*sqrt(n/3)) * (2/Pi)^(1/4) * Gamma(7/4) / (3 * 3^(5/8) * n^(9/8)). - Vaclav Kotesovec, Aug 27 2015