OFFSET
0,19
COMMENTS
A standard Young tableau (SYT) where entries i and i+1 never appear in the same row is called a nonconsecutive tableau.
LINKS
Alois P. Heinz, Antidiagonals n = 0..23, flattened
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
EXAMPLE
A(2,4) = 1:
[1 3 5 7]
[2 4 6 8].
A(4,2) = 6:
[1, 5] [1, 4] [1, 3] [1, 4] [1, 3] [1, 3]
[2, 6] [2, 6] [2, 6] [2, 5] [2, 5] [2, 4]
[3, 7] [3, 7] [4, 7] [3, 7] [4, 7] [5, 7]
[4, 8] [5, 8] [5, 8] [6, 8] [6, 8] [6, 8].
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 2, 6, 22, 92, 422, ...
1, 1, 6, 72, 1289, 29889, 831174, ...
1, 1, 18, 960, 93964, 13652068, 2621897048, ...
1, 1, 57, 14257, 8203915, 8134044455, 11865331748843, ...
MAPLE
b:= proc(l, t) option remember; local n, s; n, s:= nops(l),
add(i, i=l); `if`(s=0, 1, add(`if`(t<>i and l[i]>
`if`(i=n, 0, l[i+1]), b(subsop(i=l[i]-1, l), i), 0), i=1..n))
end:
A:= (n, k)-> `if`(n<1 or k<1, 1, b([k$n], 0)):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
b[l_, t_] := b[l, t] = Module[{n, s}, {n, s} = {Length[l], Sum[i, {i, 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_, k_] := If[n < 1 || k < 1, 1, b[Array[k&, n], 0]]; Table[Table[a[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Dec 09 2013, translated from Maple *)
CROSSREFS
Main diagonal gives A264103.
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 01 2012
STATUS
approved