A035463 - OEIS

%I #13 Aug 04 2020 13:38:57

%S 0,0,0,1,1,0,0,1,1,1,0,2,2,1,1,2,3,2,1,4,4,3,2,5,7,5,3,7,9,8,5,9,13,

%T 11,8,13,17,16,12,18,24,22,17,24,32,31,24,32,43,42,34,43,56,57,47,57,

%U 74,75,64,76,96,100,86,99,126,130,115,129,161,171,151,168,207,219,200

%N Number of partitions of n into parts 8k+4 or 8k+5.

%H Robert Price, <a href="/A035463/b035463.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(5/8) / (4 * 2^(9/16) * 3^(5/16) * Pi^(3/8) * n^(13/16)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+4))*(1 - x^(8k+5))), {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 + 5}];

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

%Y Cf. A035694.

%K nonn

%O 1,12

%A _Olivier Gérard_