A046769 Number of partitions of n with equal number of parts congruent to each of 1, 2 and 3 (mod 4).

1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 4, 0, 4, 0, 11, 0, 9, 0, 26, 0, 21, 0, 55, 0, 49, 0, 110, 0, 109, 0, 212, 0, 231, 0, 397, 0, 471, 0, 729, 0, 920, 0, 1320, 0, 1741, 0, 2357, 0, 3198, 0, 4160, 0, 5734, 0, 7258, 0, 10058, 0, 12518, 0, 17329, 0, 21346, 0, 29364, 0, 35998, 0, 49063

Offset

0,9

Links

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

Formula

G.f.: (Sum_{k>=0} x^(6*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+4)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=0, n\6, x^(6*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^3)/prod(j=0, n\4, 1 - x^(4*j+4) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A082519 A035688 A364105 * A145893 A137561 A337605

Adjacent sequences: A046766 A046767 A046768 * A046770 A046771 A046772

Keyword

nonn

Author

David W. Wilson

Status

approved