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 A213978 Number of solid standard Young tableaux of shape [[n,n,n],[n]]. 10
 1, 3, 91, 5471, 464836, 48767805, 5900575762, 791402291063, 114754560003596, 17688389169462060, 2864042102057254739, 482894371222455465001, 84225614036198359288620, 15119622005825185224290830, 2782232873996840900804273236, 523114052492282720617167786279, 100231256005025286627952024093564, 19528383010645472628217323778258916 (list; graph; refs; listen; history; text; internal format)
 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) 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

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)