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A363046 Number of partitions of n whose greatest part is a multiple of 4.

%I A363046 #19 May 21 2023 10:50:55
%S A363046 1,0,0,0,1,1,2,3,6,7,11,14,21,26,36,45,62,76,100,124,162,199,255,314,
%T A363046 399,488,612,748,932,1134,1400,1699,2086,2520,3072,3700,4488,5384,
%U A363046 6494,7766,9326,11112,13283,15778,18788,22245,26386,31150,36825,43345,51070,59953
%N A363046 Number of partitions of n whose greatest part is a multiple of 4.
%H A363046 Seiichi Manyama, <a href="/A363046/b363046.txt">Table of n, a(n) for n = 0..1000</a>
%F A363046 G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..4*k} (1-x^j).
%F A363046 a(n) ~ A000041(n)/4. - _Vaclav Kotesovec_, May 21 2023
%p A363046 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A363046      `if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i))))
%p A363046     end:
%p A363046 a:= n-> add(b(n-4*i, min(n-4*i, 4*i)), i=0..n/4):
%p A363046 seq(a(n), n=0..60);  # _Alois P. Heinz_, May 14 2023
%o A363046 (PARI) my(N=60, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k)/prod(j=1, 4*k, 1-x^j)))
%Y A363046 Column 4 of A363048.
%K A363046 nonn
%O A363046 0,7
%A A363046 _Seiichi Manyama_, May 14 2023