A373012 Number of distinct partitions p of n such that max(p) == 1 mod 3.

0, 1, 0, 0, 1, 1, 1, 3, 2, 2, 4, 3, 4, 7, 7, 8, 12, 13, 15, 20, 21, 24, 31, 34, 39, 49, 54, 62, 76, 84, 97, 116, 130, 148, 174, 195, 221, 257, 287, 325, 374, 419, 472, 540, 604, 679, 772, 861, 966, 1092, 1218, 1362, 1533, 1706, 1903, 2133, 2368, 2635, 2943, 3263, 3622, 4033, 4463

Offset

0,8

Links

Table of n, a(n) for n=0..62.

Formula

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

A000009(n) = A372893(n) + a(n) + A373013(n).

Example

a(7) = 3 counts these partitions: 7, 43, 421.

Prog

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

Crossrefs

Cf. A000009, A372893, A373013.

Sequence in context: A372490 A182214 A339505 * A351163 A216161 A332502

Adjacent sequences: A373009 A373010 A373011 * A373013 A373014 A373015

Keyword

nonn

Author

Seiichi Manyama, May 20 2024

Status

approved