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
Alois P. Heinz, Table of n, a(n) for n = 0..40
T. Y. Chow, H. Eriksson and C. K. Fan, Chess tableaux, Elect. J. Combin., 11 (2) (2005), #A3.
Wikipedia, Young tableau
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:
g:= (n, i, l)-> `if`(n=0 or i=1, b([l[], 1$n], 0)^2, `if`(i<1, 0,
add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))):
a:= n-> `if`(n<2, 1, g(n, n, [])):
seq(a(n), n=0..20);
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}]]];
g[n_, i_, l_] := If[n == 0 || i == 1, b[Join[l, Table[1, n]], 0]^2, If[i < 1, 0, Sum[g[n - i*j, i - 1, Join[l, Table[i, j]]], {j, 0, n/i}]]];
a[n_] := If[n < 2, 1, g[n, n, {}]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 23 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2012
STATUS
approved