A394022 Number of partitions p of n with multiplicity of each part at most 3, satisfying max(p) <= 2 * min(p).

1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 10, 10, 12, 14, 14, 16, 19, 20, 22, 25, 25, 29, 33, 35, 38, 42, 44, 48, 56, 58, 63, 70, 74, 80, 88, 93, 102, 111, 118, 126, 138, 145, 157, 171, 180, 194, 211, 224, 238, 256, 271, 291, 314, 333, 356, 379, 402, 429, 461, 486, 517, 552, 584, 622

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Formula

G.f.: Sum_{j>=1} q^j*(1-q^(3*j))/(1-q^j) * Product_{k=j+1..2*j} (1-q^(4*k))/(1-q^k).

Example

a(8) = 6 counts these partitions: 8, 53, 44, 422, 332, 22211.

Crossrefs

Cf. A237824, A241061, A394021.

Sequence in context: A131138 A284724 A189579 * A278617 A194640 A353086

Adjacent sequences: A394019 A394020 A394021 * A394023 A394024 A394025

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2026

Status

approved