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

1, 0, 0, 0, 1, 1, 2, 3, 6, 7, 11, 14, 21, 26, 36, 45, 62, 76, 100, 124, 162, 199, 255, 314, 399, 488, 612, 748, 932, 1134, 1400, 1699, 2086, 2520, 3072, 3700, 4488, 5384, 6494, 7766, 9326, 11112, 13283, 15778, 18788, 22245, 26386, 31150, 36825, 43345, 51070, 59953

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..4*k} (1-x^j).

a(n) ~ A000041(n)/4. - Vaclav Kotesovec, May 21 2023

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
     `if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i))))
    end:
a:= n-> add(b(n-4*i, min(n-4*i, 4*i)), i=0..n/4):
seq(a(n), n=0..60);  # Alois P. Heinz, May 14 2023

Prog

(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)))

Crossrefs

Column 4 of A363048.

Sequence in context: A018468 A117115 A308733 * A049196 A284743 A256976

Adjacent sequences: A363043 A363044 A363045 * A363047 A363048 A363049

Keyword

nonn

Author

Seiichi Manyama, May 14 2023

Status

approved