A046772 Number of partitions of n with equal number of parts congruent to each of 0, 1, 2 and 4 (mod 5).

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 5, 3, 2, 6, 4, 12, 7, 6, 17, 9, 26, 19, 14, 41, 21, 51, 47, 37, 86, 52, 99, 103, 91, 171, 115, 196, 212, 206, 328, 246, 384, 418, 437, 616, 503, 749, 793, 889, 1142, 993, 1441, 1475, 1725, 2104, 1905, 2716, 2705, 3256

Offset

0,13

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

Crossrefs

Cf. A046765.

Sequence in context: A199627 A153902 A318205 * A348291 A359652 A179974

Adjacent sequences: A046769 A046770 A046771 * A046773 A046774 A046775

Keyword

nonn

Author

David W. Wilson

Status

approved