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

0,2

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

Links

Table of n, a(n) for n=0..13.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A296624, A296626, A304662.

Sequence in context: A266124 A217194 A304662 * A156664 A025169 A111282

Adjacent sequences: A296622 A296623 A296624 * A296626 A296627 A296628

Keyword

nonn,hard,more

Author

Wouter Meeussen, Dec 17 2017

Extensions

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

Status

approved