A347867 Number of partitions of n such that 3*(greatest part) >= (number of parts).

1, 2, 3, 4, 6, 10, 14, 20, 27, 38, 51, 70, 92, 123, 162, 212, 274, 355, 453, 579, 733, 928, 1165, 1463, 1822, 2269, 2808, 3470, 4266, 5241, 6407, 7823, 9514, 11554, 13983, 16900, 20359, 24494, 29386, 35205, 42069, 50206, 59773, 71069, 84322, 99913, 118157, 139556, 164528, 193734

Offset

1,2

Comments

Also, the number of partitions of n such that (greatest part) <= 3*(number of parts).

Links

Table of n, a(n) for n=1..50.

Formula

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

Prog

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(3*k+j-1))/(1-x^j))))

Crossrefs

Cf. A064174, A237755, A347868, A347869.

Cf. A237756.

Sequence in context: A215255 A200928 A318558 * A256248 A089223 A240057

Adjacent sequences: A347864 A347865 A347866 * A347868 A347869 A347870

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2022

Status

approved