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Number of partitions of n into parts 8k+4 or 8k+6.
1

%I #11 Aug 04 2020 12:34:51

%S 0,0,0,1,0,1,0,1,0,1,0,3,0,2,0,3,0,4,0,5,0,5,0,8,0,8,0,11,0,12,0,15,0,

%T 17,0,22,0,23,0,30,0,34,0,40,0,45,0,56,0,61,0,73,0,83,0,98,0,109,0,

%U 130,0,144,0,169,0,190,0,219,0,246,0,286,0,317,0,365,0,410,0,467,0

%N Number of partitions of n into parts 8k+4 or 8k+6.

%H Robert Price, <a href="/A035464/b035464.txt">Table of n, a(n) for n = 1..1000</a>

%F If n is even, a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/4) / (2 * 6^(3/8) * Pi^(1/4) * n^(7/8)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+4))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%t nmax = 60; kmax = nmax/8;

%t s = Flatten[{Range[0, kmax]*8 + 4}~Join~{Range[0, kmax]*8 + 6}];

%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 04 2020 *)

%K nonn

%O 1,12

%A _Olivier GĂ©rard_