A213978 Number of solid standard Young tableaux of shape [[n,n,n],[n]].

1, 3, 91, 5471, 464836, 48767805, 5900575762, 791402291063, 114754560003596, 17688389169462060, 2864042102057254739, 482894371222455465001, 84225614036198359288620, 15119622005825185224290830, 2782232873996840900804273236, 523114052492282720617167786279, 100231256005025286627952024093564, 19528383010645472628217323778258916

Offset: 0

Author

N. J. A. Sloane, Jul 07 2012

Keywords

• nonn

Comments

Ekhad-Zeilberger give 121 terms.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..129
• Shalosh B. Ekhad and Doron Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux.
• S. B. Ekhad and D. Zeilberger, Number of Solid Standard Young Tableaux of shape [[n,n,n],[n]], (n=1..121); Local copy
• S. B. Ekhad and D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229, 2012

Crossrefs

Column k=3 of A214722.

Programs

Maple

b:= proc(x, y, z, u) option remember; `if`({x, y, z, u}={0}, 1,
     `if`(x>y and x>u, b(x-1, y, z, u), 0)+`if`(y>z, b(x, y-1, z, u), 0)+
     `if`(z>0, b(x, y, z-1, u), 0)+`if`(u>0, b(x, y, z, u-1), 0))
    end:
a:= n-> b(n$4):
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 19 2012

Mathematica

b[x_, y_, z_, u_] := b[x, y, z, u] = If[Union[{x, y, z, u}] == {0}, 1, If[x>y && x>u, b[x-1, y, z, u], 0] + If[y>z, b[x, y-1, z, u], 0] + If[z>0, b[x, y, z-1, u], 0] + If[u>0, b[x, y, z, u-1], 0]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 11 2014, after Alois P. Heinz *)

Formula

Conjecture: Limit n->infinity a(n)^(1/n) = 256. - Vaclav Kotesovec, Jul 17 2014