A214953 Number of solid standard Young tableaux whose shape is a 3-dimensional cube of side length n.

1, 1, 48, 6405442434150, 213896868423550025518356115338261531036549426

Offset

0,3

Links

Vasilii Duzhin, Table of n, a(n) for n = 0..5

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)[]}minus{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]):
seq(a(n), n=0..4);

Mathematica

b[l_] := b[l] = Module[{m = Length[l]}, If[Union[Flatten[l]] ~Complement~ {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[0] = 1; a[n_] := b[Table[Table[n, {n}], {n}]];
a /@ Range[0, 4] (* Jean-François Alcover, Jan 28 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A292517 A272096 A115480 * A005071 A174696 A203506

Adjacent sequences: A214950 A214951 A214952 * A214954 A214955 A214956

Keyword

nonn,more

Author

Alois P. Heinz, Jul 30 2012

Status

approved