A215220 - OEIS

%I #15 Nov 08 2017 09:53:15

%S 1,4,456,143164,75965484,55824699632,51274161733160,55418842406649988,

%T 67819708829687672202,91539069926354814114556,

%U 133752944758581353219955762,208673064320580765981337783096,343997162091593719562479905281938,594344377404793356460064021706935470

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

%H Alois P. Heinz, <a href="/A215220/b215220.txt">Table of n, a(n) for n = 0..40</a>

%H S. B. Ekhad, D. Zeilberger, <a href="https://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229v1 [math.CO], 2012

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%p b:= proc(w, x, y, z, u) option remember;

%p      `if`({w, x, y, z, u}={0}, 1, `if`(w>x and w>u, b(w-1, x, y, z, u), 0)+

%p      `if`(x>y, b(w, x-1, y, z, u), 0)+ `if`(y>z, b(w, x, y-1, z, u), 0)+

%p      `if`(z>0, b(w, x, y, z-1, u), 0)+ `if`(u>0, b(w, x, y, z, u-1), 0))

%p     end:

%p a:= n-> b(n$5):

%p seq(a(n), n=0..20);

%t b[w_, x_, y_, z_, u_] := b[w, x, y, z, u] =

%t   If[Union@{w, x, y, z, u} == {0}, 1,

%t   If[w > x && w > u, b[w - 1, x, y, z, u], 0] +

%t   If[x > y, b[w, x - 1, y, z, u], 0] +

%t   If[y > z, b[w, x, y - 1, z, u], 0] +

%t   If[z > 0, b[w, x, y, z - 1, u], 0] +

%t   If[u > 0, b[w, x, y, z, u - 1], 0]];

%t a[n_] :=  b[n, n, n, n, n];

%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Nov 08 2017, translated from Maple *)

%Y Column k=4 of A214722.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Aug 06 2012