%I #11 Aug 04 2020 21:34:35

%S 0,0,0,0,1,0,1,0,0,1,0,1,1,1,2,0,1,1,1,3,2,2,2,1,3,3,3,5,3,5,4,3,6,5,

%T 8,8,6,8,7,9,11,11,13,13,13,15,14,16,20,20,23,23,22,26,26,31,34,34,39,

%U 39,40,45,46,52,58,58,65,64,68,77,77,89,93,96,107,105,115,124,128,145

%N Number of partitions of n into parts 8k+5 or 8k+7.

%H Robert Price, <a href="/A035467/b035467.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) * Gamma(7/8) / (4 * sqrt(3*Pi) * n). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+5))*(1 - x^(8k+7))), {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 + 5}~Join~{Range[0, kmax]*8 + 7}];

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

%K nonn

%O 1,15

%A _Olivier Gérard_