A035466 - OEIS

%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_