%I #14 Aug 05 2020 02:29:29
%S 0,0,1,0,0,2,0,0,2,0,1,3,0,2,3,0,3,4,1,4,4,3,5,5,5,6,6,8,7,9,10,8,13,
%T 13,10,18,15,14,23,18,20,29,21,29,34,27,38,40,36,49,46,49,59,56,65,71,
%U 70,83,82,91,102,98,116,122,119,148,143,150,180,169,189,217,202,237
%N Number of partitions of n into parts 8k+3 or 8k+6.
%H Robert Price, <a href="/A035461/b035461.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/8) * Gamma(3/4) / (4 * 2^(9/16) * 3^(5/16) * Pi^(7/8) * n^(13/16)). - _Vaclav Kotesovec_, Aug 26 2015
%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+3))*(1 - x^(8k+6))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t nmax = 60; kmax = nmax/8;
%t s = Flatten[{Range[0, kmax]*8 + 3}~Join~{Range[0, kmax]*8 + 6}];
%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 04 2020 *)
%Y Cf. A035692.
%K nonn
%O 1,6
%A _Olivier GĂ©rard_