A035441 - OEIS

%I #14 Aug 03 2020 01:32:41

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

%T 18,23,30,35,37,38,38,38,38,45,57,66,71,73,74,74,74,85,104,121,131,

%U 136,138,139,139,154,184,212,231,241,246,248,249,271,316,363,396,416

%N Number of partitions of n into parts 8k or 8k+1.

%H Robert Price, <a href="/A035441/b035441.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(9/8) * 2^(7/16) / (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+8))*(1 - x^(8k+1))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)

%t nmax = 68; kmax = nmax/8;

%t s = Flatten[{Range[0, kmax]*8}~Join~{Range[0, kmax]*8 + 1}];

%t Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 02 2020 *)

%Y Cf. A035672.

%K nonn

%O 1,8

%A _Olivier Gérard_