A046779 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1 and 3 (mod 4).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 5, 0, 12, 0, 16, 0, 30, 0, 41, 0, 70, 0, 95, 0, 150, 0, 203, 0, 309, 0, 413, 0, 608, 0, 807, 0, 1161, 0, 1529, 0, 2154, 0, 2819, 0, 3911, 0, 5086, 0, 6951, 0, 8994, 0, 12146, 0, 15633, 0, 20881, 0, 26751, 0, 35392, 0, 45137, 0, 59197

Offset

0,13

Links

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

Formula

G.f.: (Sum_{k>0} x^(8*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+2)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\8, x^(8*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^(n-8*k)))^3)/prod(j=0, n\4, 1 - x^(4*j+2) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A200295 A352167 A089389 * A356174 A339436 A255369

Adjacent sequences: A046776 A046777 A046778 * A046780 A046781 A046782

Keyword

nonn

Author

David W. Wilson

Status

approved