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A264103 Number of n X n nonconsecutive tableaux.

%I A264103 #16 Sep 08 2021 08:56:10
%S A264103 1,1,1,6,1289,13652068,11865331748843,1232033659827201777222,
%T A264103 20955050449849509663209289613921,
%U A264103 76615072242390448445916336191834325715261848,76456972050113830615729276134092575545874371011199394401950,25770844284993968943713846068617488831241440984966512955013952234546614462044
%N A264103 Number of n X n nonconsecutive tableaux.
%C A264103 A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau.
%H A264103 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 A264103 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 A264103 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A264103 a(n) = A214021(n,n).
%e A264103 a(3) = 6:
%e A264103   [1 4 7]  [1 3 7]  [1 4 6]  [1 3 6]  [1 3 6]  [1 3 5]
%e A264103   [2 5 8]  [2 5 8]  [2 5 8]  [2 5 8]  [2 4 8]  [2 6 8]
%e A264103   [3 6 9]  [4 6 9]  [3 7 9]  [4 7 9]  [5 7 9]  [4 7 9].
%t A264103 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 A264103 a[n_] := a[n] = If[n<1, 1, b[Array[n&, n], 0]];
%t A264103 Table[Print[n, " ", a[n]]; a[n], {n, 0, 11}] (* _Jean-François Alcover_, Sep 08 2021, after _Alois P. Heinz_ in A214021 *)
%Y A264103 Main diagonal of A214021.
%K A264103 nonn
%O A264103 0,4
%A A264103 _Alois P. Heinz_, Nov 03 2015