A046766 - OEIS

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A046766

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

1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 2, 4, 1, 2, 7, 8, 2, 7, 16, 13, 7, 20, 34, 23, 20, 46, 64, 42, 51, 99, 119, 80, 115, 200, 208, 158, 249, 377, 365, 315, 498, 686, 635, 617, 960, 1213, 1105, 1188, 1770, 2093, 1924, 2228, 3171, 3554, 3351, 4072, 5523, 5965, 5808, 7262

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OFFSET

0,8

LINKS

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

FORMULA

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

PROG

(PARI) seq(n)={Vec(sum(k=0, n\7, x^(7*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^3)/prod(j=0, n\4, 1 - x^(4*j+3) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

CROSSREFS

Cf. A046765.

Sequence in context: A144172 A227318 A166692 * A292147 A003285 A059347

Adjacent sequences: A046763 A046764 A046765 * A046767 A046768 A046769

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved