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

0,15

Links

Table of n, a(n) for n=0..78.

Formula

G.f.: Sum_{k>=0} x^(3*k^2+k)/Product_{j=1..k} (1-x^j).

Mathematica

Join[{1}, Table[Count[IntegerPartitions[n], _?(#[[-1]]>3*Length[#]&)], {n, 80}]] (* Harvey P. Dale, Aug 15 2024 *)

Prog

(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)))

Crossrefs

Cf. A003106, A373073, A373075, A373076.

Cf. A350894, A373068.

Sequence in context: A157271 A025162 A330027 * A248180 A025161 A373068

Adjacent sequences: A373071 A373072 A373073 * A373075 A373076 A373077

Keyword

nonn

Author

Seiichi Manyama, May 22 2024

Status

approved