A393375 Number of partitions p of n such that 3 * (number of distinct parts of p) <= (minimal multiplicity of the parts of p).

1, 0, 0, 1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 1, 2, 3, 3, 1, 5, 2, 6, 5, 5, 4, 11, 7, 8, 10, 12, 9, 18, 12, 17, 17, 18, 19, 28, 20, 25, 26, 32, 26, 40, 30, 39, 38, 42, 37, 56, 43, 53, 50, 58, 49, 73, 57, 75, 67, 78, 68, 100, 77, 98, 97, 110, 96, 135, 110, 136, 131, 154, 137, 190, 155, 188

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Sum_{j>=0} [z^j] Product_{k>=1} (1 + z*q^(3*j*k)/(1-q^k)).

Prog

(PARI) my(N=80, q='q+O('q^N)); Vec(sum(j=0, N, polcoef(prod(k=1, N, 1+z*q^(3*j*k)/(1-q^k)), j, z)))

Crossrefs

Cf. A393298, A394188.

Sequence in context: A384212 A023645 A366769 * A167865 A218654 A054571

Adjacent sequences: A393372 A393373 A393374 * A393376 A393377 A393378

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2026

Status

approved