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

0,2

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

Formula

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

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 *)

Crossrefs

Column k=3 of A214722.

Sequence in context: A300419 A156754 A331672 * A318129 A119121 A213987

Adjacent sequences: A213975 A213976 A213977 * A213979 A213980 A213981

Keyword

nonn

Author

N. J. A. Sloane, Jul 07 2012

Status

approved