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Number of partitions of n into parts 7k or 7k+4.
0

%I #8 Aug 27 2015 06:11:06

%S 0,0,0,1,0,0,1,1,0,0,2,1,0,2,2,1,0,4,2,1,3,5,2,1,7,5,2,6,9,5,2,13,10,

%T 5,9,18,10,5,21,20,10,16,30,21,10,35,35,21,25,52,37,21,55,62,38,43,83,

%U 67,38,88,102,69,68,135,112,70,135,168,117,112,208,188,119,209,265

%N Number of partitions of n into parts 7k or 7k+4.

%F a(n) ~ exp(2*Pi*sqrt(n/21)) * 7^(1/28) * Gamma(4/7) / (4 * 3^(15/28) * Pi^(3/7) * n^(29/28)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(7k+7))*(1 - x^(7k+4))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K nonn

%O 1,11

%A _Olivier GĂ©rard_