A046767 Number of partitions of n with equal number of parts congruent to each of 0, 1 and 3 (mod 4).

1, 0, 1, 0, 1, 0, 2, 0, 3, 0, 4, 0, 8, 0, 10, 0, 18, 0, 24, 0, 40, 0, 53, 0, 85, 0, 113, 0, 172, 0, 230, 0, 341, 0, 451, 0, 654, 0, 861, 0, 1225, 0, 1605, 0, 2243, 0, 2923, 0, 4033, 0, 5228, 0, 7116, 0, 9186, 0, 12368, 0, 15889, 0, 21177, 0, 27091, 0, 35782, 0, 45585, 0, 59709

Offset

0,7

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

G.f.: (Sum_{k>=0} x^(8*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+2)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=0, n\8, x^(8*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^3)/prod(j=0, n\4, 1 - x^(4*j+2) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A008801 A073739 A223707 * A115720 A053120 A366601

Adjacent sequences: A046764 A046765 A046766 * A046768 A046769 A046770

Keyword

nonn

Author

David W. Wilson

Status

approved