A046765 Number of partitions of n with equal number of parts congruent to each of 0, 1 and 2 (mod 3).

1, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 7, 0, 0, 13, 0, 0, 25, 0, 0, 43, 0, 0, 77, 0, 0, 130, 0, 0, 222, 0, 0, 365, 0, 0, 603, 0, 0, 966, 0, 0, 1546, 0, 0, 2425, 0, 0, 3783, 0, 0, 5813, 0, 0, 8884, 0, 0, 13411, 0, 0, 20130, 0, 0, 29922, 0, 0, 44217, 0, 0, 64814, 0, 0, 94485, 0, 0

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

Other similar sequences include:

Mod 4: A046766, A046767, A046768, A046769, A046770.

Mod 5: A046771, A046772, A046773, A046774, A046775, A046776.

Programs

Mathematica

Table[Length[Select[Last /@ Transpose /@ Tally /@ Mod[IntegerPartitions[n], 3], Length[#] == 3 && Length[Union[#]] == 1 &]], {n, 50}] (* Jayanta Basu, Jun 28 2013 *)

PARI

seq(n)={Vec(sum(k=0, n\6, x^(6*k)/prod(j=1, k, 1 - x^(3*j) + O(x*x^n))^3) + O(x*x^n))} \\ Andrew Howroyd, Sep 16 2019

Formula

G.f.: Sum_{k>=0} x^(6*k)/(Product_{j=1..k} 1 - x^(3*j))^3. - Andrew Howroyd, Sep 16 2019