A046781 - OEIS

%I #9 Sep 16 2019 19:52:55

%S 0,0,0,0,0,0,1,0,0,0,4,0,1,0,11,0,4,0,26,0,14,0,55,0,38,0,110,0,94,0,

%T 212,0,209,0,397,0,441,0,729,0,878,0,1320,0,1685,0,2357,0,3121,0,4160,

%U 0,5633,0,7258,0,9923,0,12518,0,17153,0,21346,0,29133,0,35998,0,48766

%N Number of partitions of n with equal nonzero number of parts congruent to each of 1, 2 and 3 (mod 4).

%H Andrew Howroyd, <a href="/A046781/b046781.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (Sum_{k>0} x^(6*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+4)). - _Andrew Howroyd_, Sep 16 2019

%o (PARI) seq(n)={Vec(sum(k=1, n\6, x^(6*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^(n-6*k)))^3)/prod(j=0, n\4, 1 - x^(4*j+4) + O(x*x^n)), -(n+1))} \\ _Andrew Howroyd_, Sep 16 2019

%Y Cf. A046787.

%K nonn

%O 0,11

%A _David W. Wilson_