A046784 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1, 2 and 4 (mod 5).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 4, 1, 0, 5, 1, 10, 5, 2, 15, 5, 22, 16, 9, 37, 16, 45, 42, 30, 80, 44, 91, 96, 80, 162, 105, 183, 202, 192, 314, 232, 367, 402, 418, 597, 483, 725, 772, 862, 1115, 966, 1408, 1445, 1690, 2066, 1869, 2672, 2663, 3209, 3777

Offset

0,18

Links

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

Formula

G.f.: (Sum_{k>0} x^(12*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+3)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\12, x^(12*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^(n-12*k)))^4)/prod(j=0, n\5, 1 - x^(5*j+3) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A303499 A108944 A117377 * A011349 A303126 A292404

Adjacent sequences: A046781 A046782 A046783 * A046785 A046786 A046787

Keyword

nonn

Author

David W. Wilson

Status

approved