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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 03 2015
STATUS
approved