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

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

Cf. A046787.

Programs

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

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