A046773 Number of partitions of n with equal number of parts congruent to each of 0, 1, 3 and 4 (mod 5).

1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3, 7, 4, 8, 5, 9, 15, 11, 20, 13, 22, 34, 24, 49, 30, 55, 67, 59, 103, 76, 120, 139, 129, 211, 170, 253, 276, 277, 409, 373, 498, 554, 558, 787, 762, 962, 1079, 1100, 1475, 1513, 1799, 2079, 2095, 2747, 2882, 3325

Offset

0,13

Links

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

Formula

G.f.: (Sum_{k>=0} x^(13*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+2)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=0, n\13, x^(13*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^n))^4)/prod(j=0, n\5, 1 - x^(5*j+2) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A204597 A285734 A051698 * A175402 A281726 A101037

Adjacent sequences: A046770 A046771 A046772 * A046774 A046775 A046776

Keyword

nonn

Author

David W. Wilson

Status

approved