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%I #11 Aug 04 2020 21:33:28
%S 0,0,0,0,1,1,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,4,5,5,6,6,7,
%T 8,8,8,9,10,12,12,14,14,15,16,17,19,22,22,24,25,27,29,32,34,38,39,42,
%U 44,48,51,55,59,64,67,72,75,81,87,94,99,107,111,119,126,135,144,154
%N Number of partitions of n into parts 8k+5 or 8k+6.
%H Robert Price, <a href="/A035466/b035466.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) * Gamma(3/4) / (4 * 2^(3/16) * 3^(7/16) * Pi^(5/8) * n^(15/16)). - _Vaclav Kotesovec_, Aug 27 2015
%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+5))*(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 + 5}~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 1,18
%A _Olivier Gérard_