A387259 Number of unordered pairs of partitions of n with the same number of parts.

1, 1, 2, 3, 6, 9, 18, 28, 52, 86, 151, 246, 431, 694, 1167, 1884, 3095, 4904, 7919, 12379, 19596, 30315, 47117, 71922, 110332, 166403, 251547, 375575, 560787, 828276, 1223544, 1789656, 2616001, 3793295, 5491711, 7895309, 11333811, 16164595, 23013551, 32584816

Offset

0,3

Comments

The corresponding sequence for ordered pairs of partitions is A238312.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} A000217(A072233(n,k)).

a(n) = A380126(n) - A380124(n).

Example

For example, a(4)=6: (4,4) (3+1,3+1) (3+1,2+2) (2+2,2+2) (2+1+1,2+1+1) (1+1+1+1,1+1+1+1).
Note that (3+1,2+2) and (2+2,3+1) are not both counted.

Crossrefs

Cf. A380124, A380126, A008284, A072233, A238312.

Sequence in context: A038754 A182522 A165647 * A191398 A066313 A224958

Adjacent sequences: A387256 A387257 A387258 * A387260 A387261 A387262

Keyword

nonn

Author

Aidan Markey, Aug 24 2025

Status

approved