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Number of partitions of n with equal number of parts congruent to each of 0, 1 and 3 (mod 4).
2

%I #9 Sep 16 2019 17:04:25

%S 1,0,1,0,1,0,2,0,3,0,4,0,8,0,10,0,18,0,24,0,40,0,53,0,85,0,113,0,172,

%T 0,230,0,341,0,451,0,654,0,861,0,1225,0,1605,0,2243,0,2923,0,4033,0,

%U 5228,0,7116,0,9186,0,12368,0,15889,0,21177,0,27091,0,35782,0,45585,0,59709

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

%H Andrew Howroyd, <a href="/A046767/b046767.txt">Table of n, a(n) for n = 0..1000</a>

%F 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

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

%Y Cf. A046765.

%K nonn

%O 0,7

%A _David W. Wilson_