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Number of partitions of n into parts 4k+1 or 4k+2.
1

%I #8 Aug 27 2015 05:51:24

%S 1,2,2,3,4,6,7,9,11,15,18,23,27,34,41,50,59,72,85,103,120,143,167,198,

%T 230,270,313,366,422,491,564,653,748,861,984,1130,1287,1471,1671,1905,

%U 2159,2453,2772,3141,3544,4004,4506,5079,5705,6416,7192,8070,9030

%N Number of partitions of n into parts 4k+1 or 4k+2.

%F a(n) ~ exp(Pi*sqrt(n/3)) * Gamma(5/4) / (3^(1/8) * (2*Pi)^(3/4) * n^(5/8)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(4k+1))*(1 - x^(4k+2))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K nonn

%O 1,2

%A _Olivier GĂ©rard_