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
Keywords
Programs
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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).