A264103 Number of n X n nonconsecutive tableaux.

1, 1, 1, 6, 1289, 13652068, 11865331748843, 1232033659827201777222, 20955050449849509663209289613921, 76615072242390448445916336191834325715261848, 76456972050113830615729276134092575545874371011199394401950, 25770844284993968943713846068617488831241440984966512955013952234546614462044

Offset

0,4

Comments

A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau.

Links

Table of n, a(n) for n=0..11.

T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3.

S. Dulucq and O. Guibert, Stack words, standard tableaux and Baxter permutations, Disc. Math. 157 (1996), 91-106.

Wikipedia, Young tableau

Formula

a(n) = A214021(n,n).

Example

a(3) = 6:
  [1 4 7]  [1 3 7]  [1 4 6]  [1 3 6]  [1 3 6]  [1 3 5]
  [2 5 8]  [2 5 8]  [2 5 8]  [2 5 8]  [2 4 8]  [2 6 8]
  [3 6 9]  [4 6 9]  [3 7 9]  [4 7 9]  [5 7 9]  [4 7 9].

Mathematica

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}]]];
a[n_] := a[n] = If[n<1, 1, b[Array[n&, n], 0]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 11}] (* Jean-François Alcover, Sep 08 2021, after Alois P. Heinz in A214021 *)

Crossrefs

Main diagonal of A214021.

Sequence in context: A183585 A060706 A052278 * A202381 A067510 A013738

Adjacent sequences: A264100 A264101 A264102 * A264104 A264105 A264106

Keyword

nonn

Author

Alois P. Heinz, Nov 03 2015

Status

approved