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Number of partitions of n into parts 6k+2 or 6k+4.
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%I #12 Aug 27 2015 06:05:48

%S 1,0,1,0,2,0,2,0,4,0,5,0,7,0,9,0,13,0,16,0,22,0,27,0,36,0,44,0,57,0,

%T 70,0,89,0,108,0,135,0,163,0,202,0,243,0,297,0,355,0,431,0,513,0,617,

%U 0,731,0,874,0,1031,0,1225,0,1439,0,1701,0,1991,0,2341,0,2731,0,3197,0

%N Number of partitions of n into parts 6k+2 or 6k+4.

%F a(2*n) = A000726(n). a(2*n + 1) = 0. - _Michael Somos_, Jun 02 2012

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

%t nmax = 100; CoefficientList[Series[Product[1/((1 - x^(6k+2))*(1 - x^(6k+4))), {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%Y Cf. A000726.

%K nonn

%O 0,5

%A _Olivier GĂ©rard_