A046765 - OEIS

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

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OFFSET

0,10

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Other similar sequences include:

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

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

Sequence in context: A060284 A036275 A131436 * A046777 A227724 A218538

Adjacent sequences: A046762 A046763 A046764 * A046766 A046767 A046768

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved