A214638 Number of solid standard Young tableaux of shape [[n,n,n],[n],[n]].

1, 6, 936, 379366, 249664758, 221005209058, 239143562020194, 299233941746052998, 417999868371999142276, 636568066798406010872120, 1039267652960081699025215774, 1796704965351078502372895796786, 3258764657213579008313421745034602

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012

Wikipedia, Young tableau

Maple

b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>
      `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
       j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
    end:
a:= n-> b([[n, n, n], [n], [n]]):
seq(a(n), n=0..10);

Mathematica

b[l_] := b[l] = With[{m := Length[l]}, If[Union[Flatten[l]] == {0}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i+1]]] < j, 0, l[[i+1, j]]] && l[[i, j]] > If[Length[l[[i]]] == j, 0, l[[i, j+1]]], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]]-1]]], 0], {j, 1, Length[l[[i]]]}], {i, 1, m}]] ]; a[n_] := b[{{n, n, n}, {n}, {n}}]; Table[a[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Dec 18 2013, translated from Maple *)

Crossrefs

Cf. A213932, A213978, A214637.

Sequence in context: A137801 A076667 A000652 * A175554 A263423 A266598

Adjacent sequences: A214635 A214636 A214637 * A214639 A214640 A214641

Keyword

nonn

Author

Alois P. Heinz, Jul 23 2012

Status

approved