A046781 Number of partitions of n with equal nonzero number of parts congruent to each of 1, 2 and 3 (mod 4).

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 1, 0, 11, 0, 4, 0, 26, 0, 14, 0, 55, 0, 38, 0, 110, 0, 94, 0, 212, 0, 209, 0, 397, 0, 441, 0, 729, 0, 878, 0, 1320, 0, 1685, 0, 2357, 0, 3121, 0, 4160, 0, 5633, 0, 7258, 0, 9923, 0, 12518, 0, 17153, 0, 21346, 0, 29133, 0, 35998, 0, 48766

Offset

0,11

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

Crossrefs

Cf. A046787.

Sequence in context: A344373 A325873 A363973 * A244530 A271424 A117435

Adjacent sequences: A046778 A046779 A046780 * A046782 A046783 A046784

Keyword

nonn

Author

David W. Wilson

Status

approved