A373013 Number of distinct partitions p of n such that max(p) == 2 mod 3.

0, 0, 1, 1, 0, 1, 1, 1, 3, 3, 3, 5, 5, 5, 8, 9, 9, 13, 15, 17, 23, 26, 29, 36, 41, 46, 57, 64, 72, 87, 98, 111, 131, 149, 168, 197, 223, 251, 291, 328, 369, 423, 476, 534, 609, 683, 765, 867, 970, 1084, 1222, 1365, 1522, 1710, 1905, 2121, 2374, 2639, 2931, 3269, 3627, 4020, 4471, 4950

Offset

0,9

Links

Table of n, a(n) for n=0..63.

Formula

G.f.: Sum_{k>=0} x^(3*k+2) * Product_{j=1..3*k+1} (1+x^j).

A000009(n) = A372893(n) + A373012(n) + a(n).

Example

a(8) = 3 counts these partitions: 8, 53, 521.

Prog

(PARI) my(N=70, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)*prod(j=1, 3*k+1, 1+x^j))))

Crossrefs

Cf. A000009, A372893, A373012.

Sequence in context: A080605 A130823 A101435 * A077886 A096015 A046702

Adjacent sequences: A373010 A373011 A373012 * A373014 A373015 A373016

Keyword

nonn

Author

Seiichi Manyama, May 20 2024

Status

approved