A373074 Number of partitions of n such that (smallest part) > 3*(number of parts).
1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 11, 11, 13, 14, 16, 17, 20, 21, 24, 26, 29, 31, 35, 37, 41, 44, 48, 51, 56, 59, 64, 68, 74, 78, 85, 90, 98, 104, 113, 120, 131, 139, 151, 161, 175, 186, 202, 215, 233, 248, 268, 285, 308, 327, 352, 374, 402, 426, 457
Offset: 0
Keywords
Programs
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Mathematica
Join[{1},Table[Count[IntegerPartitions[n],?(#[[-1]]>3*Length[#]&)],{n,80}]] (* _Harvey P. Dale, Aug 15 2024 *) -
PARI
my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k^2+k)/prod(j=1, k, 1-x^j)))
Formula
G.f.: Sum_{k>=0} x^(3*k^2+k)/Product_{j=1..k} (1-x^j).