A046780 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 2 and 3 (mod 4).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 5, 5, 5, 11, 16, 17, 17, 27, 40, 45, 46, 61, 90, 106, 111, 133, 187, 227, 243, 276, 372, 459, 503, 555, 713, 887, 989, 1078, 1333, 1656, 1877, 2039, 2437, 3008, 3449, 3755, 4376, 5345, 6185, 6765, 7731, 9324, 10844

Offset

0,14

Links

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

Formula

G.f.: (Sum_{k>0} x^(9*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+1)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\9, x^(9*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^(n-9*k)))^3)/prod(j=0, n\4, 1 - x^(4*j+1) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A088202 A238187 A307109 * A075129 A021691 A248926

Adjacent sequences: A046777 A046778 A046779 * A046781 A046782 A046783

Keyword

nonn

Author

David W. Wilson

Status

approved