login
A046779
Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1 and 3 (mod 4).
2
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
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
KEYWORD
nonn
STATUS
approved