%I #16 Sep 08 2021 08:56:10
%S 1,1,1,6,1289,13652068,11865331748843,1232033659827201777222,
%T 20955050449849509663209289613921,
%U 76615072242390448445916336191834325715261848,76456972050113830615729276134092575545874371011199394401950,25770844284993968943713846068617488831241440984966512955013952234546614462044
%N Number of n X n nonconsecutive tableaux.
%C A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau.
%H T. Y. Chow, H. Eriksson and C. K. Fan, <a href="http://www.combinatorics.org/Volume_11/Abstracts/v11i2a3.html">Chess tableaux</a>, Elect. J. Combin., 11 (2) (2005), #A3.
%H S. Dulucq and O. Guibert, <a href="https://doi.org/10.1016/S0012-365X(96)83009-3">Stack words, standard tableaux and Baxter permutations</a>, Disc. Math. 157 (1996), 91-106.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F a(n) = A214021(n,n).
%e a(3) = 6:
%e [1 4 7] [1 3 7] [1 4 6] [1 3 6] [1 3 6] [1 3 5]
%e [2 5 8] [2 5 8] [2 5 8] [2 5 8] [2 4 8] [2 6 8]
%e [3 6 9] [4 6 9] [3 7 9] [4 7 9] [5 7 9] [4 7 9].
%t b[l_, t_] := b[l, t] = Module[{n = Length[l], s = Total[l]}, If[s == 0, 1, Sum[If[t != i && l[[i]] > If[i == n, 0, l[[i+1]]], b[ReplacePart[l, i -> l[[i]]-1], i], 0], {i, 1, n}]]];
%t a[n_] := a[n] = If[n<1, 1, b[Array[n&, n], 0]];
%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 11}] (* _Jean-François Alcover_, Sep 08 2021, after _Alois P. Heinz_ in A214021 *)
%Y Main diagonal of A214021.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Nov 03 2015
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