A046768 Number of partitions of n with equal number of parts congruent to each of 0, 2 and 3 (mod 4).

1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 9, 11, 12, 12, 19, 26, 28, 29, 40, 55, 62, 64, 81, 113, 132, 139, 163, 221, 265, 284, 320, 421, 514, 563, 619, 783, 965, 1074, 1169, 1432, 1765, 1996, 2167, 2575, 3159, 3613, 3931, 4566, 5552, 6410, 7006, 7990, 9605

Offset

0,6

Links

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

Formula

G.f.: (Sum_{k>=0} x^(9*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+1)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=0, n\9, x^(9*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^3)/prod(j=0, n\4, 1 - x^(4*j+1) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A131799 A078635 A286305 * A363405 A274151 A216393

Adjacent sequences: A046765 A046766 A046767 * A046769 A046770 A046771

Keyword

nonn

Author

David W. Wilson

Status

approved