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A296624 a(n) is the total multiplicity of all products of Schur functions s(lambda)*s(mu) with partition lambda >= mu and size(lambda) + size(mu)= n. 3
1, 1, 4, 7, 20, 37, 90, 171, 378, 721, 1500, 2843, 5682, 10661, 20674 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The condition lambda >= mu restricts the results to the lower triangular part of the matrix formed by products of all pairs of partitions.

'Multiplicity' signifies that terms like k*s(nu) count as k terms.

LINKS

Table of n, a(n) for n=0..14.

Wouter Meeussen, Mathematica toolbox for symmetric functions

EXAMPLE

For n=3 we have

s(3)*s(0) = s(3); s(2,1)*s(0) = s(2,1); s(1,1,1)*s(0) = s(1,1,1)

s(2)*s(1) = s(3) + s(2,1) and

s(1,1)*s(1) = s(2,1) + s(1,1,1)

for a total of 3+2+2 = 7 terms.

MATHEMATICA

Tr/@ Table[Sum[

  Length[LRRule[\[Lambda], \[Mu]]], {\[Lambda],

   Partitions[n - i]}, {\[Mu],

   If[2 i === n, Join[{\[Lambda]}, lesspartitions[\[Lambda]]],

    Partitions[i]]}], {n, 14}, {i, 0, Floor[(n)/2]}]; (* Uses functions defined in the 'Toolbox for symmetric functions', see Links. *)

CROSSREFS

Cf. A296625, A296626.

Sequence in context: A147065 A049947 A266822 * A296663 A066345 A026570

Adjacent sequences:  A296621 A296622 A296623 * A296625 A296626 A296627

KEYWORD

nonn,hard,more

AUTHOR

Wouter Meeussen, Dec 17 2017

STATUS

approved

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Last modified May 18 21:30 EDT 2022. Contains 353825 sequences. (Running on oeis4.)