A296625 a(n) is the total multiplicity of all products of Schur functions s(lambda)*s(lambda) with lambda a partition of n.

1, 2, 6, 16, 42, 106, 268, 660, 1618, 3922, 9438, 22540, 53528, 126358

Offset: 0

Author

Wouter Meeussen, Dec 17 2017

Keywords

• nonn
• hard
• more

Comments

Diagonal of the matrix formed by products of all pairs of partitions.

Conjecture: a(n) is the number of domino tilings of diagrams of integer partitions of 2n. - Gus Wiseman, Feb 25 2018

The above conjecture is not true, see A304662. - Alois P. Heinz, May 22 2018

Examples

			for n=2,
s(2)*s(2) = s(4) + s(3,1) + s(2,2) and
s(1,1) * s(1,1) = s(2,2) + s(2,1,1) + s(1,1,1,1)
for 6 terms in total.
		

Crossrefs

Cf. A296624, A296626, A304662.

Programs

Mathematica

Table[Sum[Length[LRRule[\[Lambda], \[Lambda]]], {\[Lambda], Partitions[n]}], {n, 0, 7}];
(* Uses the Mathematica toolbox for Symmetric Functions from A296624. *)

Formula

a(n) = A304662(n) for n < 7. - Alois P. Heinz, May 22 2018

Extensions

a(13)-a(14) from Wouter Meeussen, Nov 22 2018