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

Author

Aidan Markey, Aug 24 2025

Keywords

• nonn
• new

Comments

The corresponding sequence for ordered pairs of partitions is A238312.

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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

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