A238589 Number of partitions p of n such that 2*min(p) is a part of p.

0, 0, 1, 1, 2, 4, 5, 8, 13, 17, 24, 36, 47, 64, 88, 116, 153, 203, 261, 340, 439, 559, 710, 905, 1136, 1427, 1786, 2223, 2756, 3415, 4201, 5167, 6330, 7730, 9413, 11449, 13864, 16767, 20225, 24344, 29228, 35045, 41898, 50029, 59609, 70899, 84165, 99785, 118052

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000041(n) - A238594(n).

G.f.: Sum_{k>=1} x^(3*k)/Product_{j>=k} (1-x^j). - Seiichi Manyama, May 17 2023

Example

a(6) counts these partitions:  42, 321, 2211, 21111.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 50}]

Prog

(PARI) my(N=50, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/prod(j=k, N, 1-x^j)))) \\ Seiichi Manyama, May 17 2023

Crossrefs

Cf. A117989, A238590, A238591.

Cf. A118096, A238479, A238594.

Sequence in context: A178656 A085443 A164571 * A327045 A288668 A264800

Adjacent sequences: A238586 A238587 A238588 * A238590 A238591 A238592

Keyword

nonn,easy

Author

Clark Kimberling, Mar 01 2014

Status

approved