A052810 a(n) = 1 + (number of partitions of n, n>0).

1, 2, 3, 4, 6, 8, 12, 16, 23, 31, 43, 57, 78, 102, 136, 177, 232, 298, 386, 491, 628, 793, 1003, 1256, 1576, 1959, 2437, 3011, 3719, 4566, 5605, 6843, 8350, 10144, 12311, 14884, 17978, 21638, 26016, 31186, 37339, 44584, 53175, 63262, 75176, 89135

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

For n>0: number of occurrences of n in partitions of 2*n: a(n)=A066633(2*n,n), cf. A058696. - Reinhard Zumkeller, Feb 22 2004

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 772.

Crossrefs

Cf. A000041, A057427.

Programs

Maple

spec := [S,{B=Set(C),C=Sequence(Z,1 <= card), S = Union(C,B)}, unlabeled]:
seq(combstruct[count](spec, size=n), n=0..20);
A052810 := n -> combinat:-numbpart(n) + ifelse(n=0, 0, 1):
seq(A052810(i), i=0..50);

Mathematica

Join[{1}, PartitionsP[Range[50]] + 1] (* Paolo Xausa, Jun 21 2024 *)

Formula

G.f.: exp(Sum_{j >= 1} (x^j)/(1 - x^j)/j) - x/(x - 1). [Simplified by Paolo Xausa, Jun 21 2024]

a(n) = A000041(n) + A057427(n). - Alois P. Heinz, May 14 2023

Extensions

Better description and more terms from Vladeta Jovovic, Oct 06 2001