cp's OEIS Frontend

A035454 Number of partitions of n into parts 8k+2 or 8k+3.

%I A035454 #18 Aug 04 2020 08:44:52
%S A035454 0,1,1,1,1,2,1,2,2,3,3,4,4,5,5,6,6,8,8,10,11,13,13,16,16,19,20,23,25,
%T A035454 29,30,35,37,41,44,50,53,60,64,72,76,85,90,100,107,118,126,140,148,
%U A035454 163,174,190,203,223,237,260,277,301,321,349,371,403,430,466,496,537
%N A035454 Number of partitions of n into parts 8k+2 or 8k+3.
%H A035454 Robert Israel, <a href="/A035454/b035454.txt">Table of n, a(n) for n = 1..10000</a>
%F A035454 a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/4) * Gamma(3/8) / (8 * 2^(5/16) * 3^(1/16) * Pi^(11/8) * n^(9/16)). - _Vaclav Kotesovec_, Aug 26 2015
%F A035454 G.f.: Product_{k>=0} 1/((1-x^(8*k+2))*(1-x^(8*k+3))). - _Robert Israel_, Dec 11 2018
%p A035454 nmax:= 100:
%p A035454 g:= mul(1/(1-x^(8*k+2))/(1-x^(8*k+3)),k=0..(nmax-2)/8):
%p A035454 S:= series(g,x,nmax+1):
%p A035454 seq(coeff(S,x,j),j=1..nmax); # _Robert Israel_, Dec 11 2018
%t A035454 nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 26 2015 *)
%t A035454 nmax = 60; kmax = nmax/8;
%t A035454 s = Flatten[{Range[0, kmax]*8 + 2}~Join~{Range[0, kmax]*8 + 3}];
%t A035454 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* _Robert Price_, Aug 03 2020 *)
%Y A035454 Cf. A035685.
%K A035454 nonn
%O A035454 1,6
%A A035454 _Olivier Gérard_