A363211 Number of partitions of n such that 3*(least part) <= greatest part.

0, 0, 0, 1, 2, 4, 7, 12, 18, 27, 39, 56, 78, 106, 143, 193, 254, 333, 432, 560, 717, 914, 1157, 1461, 1833, 2292, 2849, 3536, 4362, 5372, 6587, 8062, 9825, 11951, 14487, 17533, 21150, 25469, 30583, 36670, 43850, 52357, 62366, 74184, 88048, 104359, 123442, 145826, 171946, 202487

Offset: 1

Author

Seiichi Manyama, May 27 2023

Keywords

• nonn

Crossrefs

Cf. A237821, A363276.

Cf. A237825, A363075.

Programs

Mathematica

Table[Count[IntegerPartitions[n],?(3#[[-1]]<=#[[1]]&)],{n,50}] (* _Harvey P. Dale, Aug 03 2025 *)

Formula

G.f.: Sum_{i>=1} Sum_{j>=0} x^(4*i+j) /Product_{k=i..3*i+j} (1-x^k).