A046783 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1, 2 and 3 (mod 5).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 4, 0, 0, 1, 5, 10, 1, 1, 5, 15, 21, 5, 5, 16, 36, 41, 19, 17, 41, 76, 80, 53, 46, 92, 151, 156, 132, 111, 192, 287, 307, 293, 248, 378, 537, 599, 616, 521, 722, 990, 1158, 1220, 1051, 1346, 1818, 2191, 2339, 2050, 2481, 3302

Offset

0,17

Links

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

Formula

G.f.: (Sum_{k>0} x^(11*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+4)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\11, x^(11*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^(n-11*k)))^4)/prod(j=0, n\5, 1 - x^(5*j+4) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A335951 A254156 A344386 * A134832 A123163 A194794

Adjacent sequences: A046780 A046781 A046782 * A046784 A046785 A046786

Keyword

nonn

Author

David W. Wilson

Status

approved