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Number of partitions of n into parts 4k or 4k+3.
2

%I #8 Aug 27 2015 05:50:27

%S 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,

%T 38,58,67,62,68,95,108,103,114,155,172,166,188,246,268,264,303,384,

%U 413,415,477,588,630,640,737,893,948,975,1125,1333,1412,1470,1688

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

%F 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

%t 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 *)

%K nonn

%O 1,7

%A _Olivier GĂ©rard_