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A046778
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Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1 and 2 (mod 4).
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2
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0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 3, 0, 1, 5, 6, 1, 5, 13, 11, 5, 16, 30, 20, 16, 41, 59, 37, 45, 92, 111, 73, 107, 189, 198, 148, 236, 363, 351, 300, 481, 667, 615, 597, 936, 1186, 1079, 1160, 1737, 2058, 1889, 2189, 3127, 3508, 3303, 4020, 5465, 5903, 5745, 7193
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OFFSET
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0,12
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LINKS
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FORMULA
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G.f.: (Sum_{k>0} x^(7*k)/(Product_{j=1..k} 1 - x^(4*j))^3)/(Product_{j>=0} 1 - x^(4*j+3)). - Andrew Howroyd, Sep 16 2019
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PROG
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(PARI) seq(n)={Vec(sum(k=1, n\7, x^(7*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^(n-7*k)))^3)/prod(j=0, n\4, 1 - x^(4*j+3) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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