A035442 - OEIS

%I #14 Aug 03 2020 18:27:36

%S 0,1,0,1,0,1,0,2,0,3,0,3,0,3,0,5,0,7,0,8,0,8,0,11,0,15,0,17,0,18,0,23,

%T 0,30,0,35,0,37,0,45,0,57,0,66,0,71,0,84,0,104,0,121,0,131,0,151,0,

%U 183,0,212,0,231,0,263,0,313,0,362,0,396,0,446,0,523,0,601,0,660,0

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

%H Robert Price, <a href="/A035442/b035442.txt">Table of n, a(n) for n = 1..1000</a>

%F If n is even, a(n) ~ 2 * exp(Pi*sqrt(n/6)) * Gamma(5/4) / (6^(3/8) * Pi^(3/4) * n^(7/8)). - _Vaclav Kotesovec_, Aug 26 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+8))*(1 - x^(8k+2))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)

%t nmax = 50; kmax = nmax/8;

%t s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 2}];

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

%Y Cf. A035679.

%K nonn

%O 1,8

%A _Olivier Gérard_