A046770 Number of partitions of n with equal number of parts congruent to each of 0, 1, 2 and 3 (mod 4).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 10, 0, 1, 0, 20, 0, 4, 0, 35, 0, 14, 0, 57, 0, 36, 0, 88, 0, 85, 0, 134, 0, 177, 0, 205, 0, 348, 0, 321, 0, 638, 0, 519, 0, 1126, 0, 866, 0, 1905, 0, 1473, 0, 3141, 0, 2530, 0, 5046, 0, 4341, 0, 7976, 0, 7387, 0, 12416, 0, 12415

Offset

0,15

Links

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

Formula

G.f.: Sum_{k>=0} x^(10*k)/(Product_{j=1..k} 1 - x^(4*j))^4. - Andrew Howroyd, Sep 16 2019

Mathematica

kmax = 75; Sum[x^(10k)/Product[1 - x^(4j), {j, 1, k}]^4, {k, 0, kmax}] + O[x]^kmax // CoefficientList[#, x]& (* Jean-François Alcover, Sep 23 2019 *)

Prog

(PARI) seq(n)={Vec(sum(k=0, n\10, x^(10*k)/prod(j=1, k, 1 - x^(4*j) + O(x*x^n))^4) + O(x*x^n))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A327054 A101419 A060278 * A046782 A074037 A285132

Adjacent sequences: A046767 A046768 A046769 * A046771 A046772 A046773

Keyword

nonn

Author

David W. Wilson

Status

approved