A296624 -id:A296624 - cp's OEIS frontend

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

Wouter Meeussen, Dec 17 2017

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

			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.

Cf. A296624, A296626, A304662.

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

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

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

A296626 a(n) is the total multiplicity of all products of Schur functions s(lambda)*s(mu) with size(lambda) + size(mu) = n.

Original entry on oeis.org

1, 2, 6, 14, 34, 74, 164, 342, 714, 1442, 2894, 5686, 11096, 21322, 40688

Offset: 0

Wouter Meeussen, Dec 17 2017

Equals 2*A296624 - aerated version of A296625, so s(lambda)*s(mu) is counted again as s(mu)*s(lambda) if mu <> lambda. The aerated version of A296625 reads as 1, 0, 2, 0, 6, 0, 16, 0, 42, 0, 106, 0, ...

For a program see A296624 and A296625.

cp's OEIS Frontend

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

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