A035455 - OEIS

%I #13 Aug 04 2020 06:38:41

%S 0,1,0,2,0,2,0,3,0,4,0,6,0,7,0,9,0,11,0,15,0,18,0,23,0,27,0,34,0,41,0,

%T 50,0,59,0,72,0,85,0,103,0,120,0,143,0,167,0,198,0,230,0,270,0,313,0,

%U 366,0,422,0,491,0,564,0,653,0,748,0,861,0,984,0,1130,0,1287,0,1471,0

%N Number of partitions of n into parts 8k+2 or 8k+4.

%H Robert Price, <a href="/A035455/b035455.txt">Table of n, a(n) for n = 1..1000</a>

%F If n is even, a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/4) / (4 * 6^(1/8) * Pi^(3/4) * n^(5/8)). - _Vaclav Kotesovec_, Aug 26 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+4))), {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 + 2}~Join~{Range[0, kmax]*8 + 4}];

%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)

%Y Cf. A035686.

%K nonn

%O 1,4

%A _Olivier Gérard_