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

%I A213978 #32 Mar 29 2021 14:16:59
%S A213978 1,3,91,5471,464836,48767805,5900575762,791402291063,114754560003596,
%T A213978 17688389169462060,2864042102057254739,482894371222455465001,
%U A213978 84225614036198359288620,15119622005825185224290830,2782232873996840900804273236,523114052492282720617167786279,100231256005025286627952024093564,19528383010645472628217323778258916
%N A213978 Number of solid standard Young tableaux of shape [[n,n,n],[n]].
%C A213978 Ekhad-Zeilberger give 121 terms.
%H A213978 Alois P. Heinz, <a href="/A213978/b213978.txt">Table of n, a(n) for n = 0..129</a>
%H A213978 Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ssyt.html">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>.
%H A213978 S. B. Ekhad and D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/tokhniot/oSolidSYT7">Number of Solid Standard Young Tableaux of shape [[n,n,n],[n]]</a>, (n=1..121); <a href="/A213978/a213978.txt">Local copy</a>
%H A213978 S. B. Ekhad and D. Zeilberger, <a href="http://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229, 2012
%F A213978 Conjecture: Limit n->infinity a(n)^(1/n) = 256. - _Vaclav Kotesovec_, Jul 17 2014
%p A213978 b:= proc(x, y, z, u) option remember; `if`({x, y, z, u}={0}, 1,
%p A213978      `if`(x>y and x>u, b(x-1, y, z, u), 0)+`if`(y>z, b(x, y-1, z, u), 0)+
%p A213978      `if`(z>0, b(x, y, z-1, u), 0)+`if`(u>0, b(x, y, z, u-1), 0))
%p A213978     end:
%p A213978 a:= n-> b(n$4):
%p A213978 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 19 2012
%t A213978 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_ *)
%Y A213978 Column k=3 of A214722.
%K A213978 nonn
%O A213978 0,2
%A A213978 _N. J. A. Sloane_, Jul 07 2012