OFFSET
0,8
LINKS
Alois P. Heinz, Antidiagonals n = 0..18, flattened
EXAMPLE
A(2,2) = 2^2 = 4:
(1,2) (0,1)
/ \ / \
(2,2) (1,1) (0,0)
\ / \ /
(2,1) (1,0)
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 2, 6, 24, 120, ...
1, 1, 4, 44, 896, 29392, ...
1, 1, 8, 320, 33904, 7453320, ...
1, 1, 16, 2328, 1281696, 1897242448, ...
1, 1, 32, 16936, 48447504, 482913033152, ...
MAPLE
b:= proc(l) option remember; `if`({l[]}={0}, 1, add(
`if`(l[i]=0 or i>1 and 1<abs(l[i-1]-l[i]+1) or
i<nops(l) and 1<abs(l[i+1]-l[i]+1), 0,
b(subsop(i=l[i]-1, l))), i=1..nops(l)))
end:
A:= (n, k)-> `if`(k<2, 1, b([n$k])):
seq(seq(A(n, d-n), n=0..d), d=0..10);
MATHEMATICA
b[l_] := b[l] = If[Union[l] == {0}, 1, Sum[If[l[[i]] == 0 || i>1 && 1 < Abs[l[[i-1]] - l[[i]] + 1] || i<Length[l] && 1<Abs[l[[i+1]] - l[[i]] + 1], 0, b[ReplacePart[l, i -> l[[i]]-1]]], {i, 1, Length[l]}]]; a[n_, k_] := If[k<2, 1, b[Array[n&, k]]]; Table[Table[a[n, d - n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Dec 12 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 19 2013
STATUS
approved