OFFSET
0,9
LINKS
Alois P. Heinz, Antidiagonals n = 0..60, flattened
FORMULA
A(n,k) == 1 (mod k) for k >= 2.
EXAMPLE
A(2,2) = 3: [(0,0),(1,1),(2,2)], [(0,0),(1,1),(0,1)], [(0,0),(1,1),(1,0)].
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, 8, ...
1, 3, 7, 13, 21, 31, 43, 57, ...
1, 6, 17, 40, 81, 146, 241, 372, ...
1, 10, 47, 136, 325, 686, 1315, 2332, ...
1, 20, 125, 496, 1433, 3476, 7525, 14960, ...
1, 35, 333, 1753, 6473, 18711, 46165, 102173, ...
...
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1, b(n-1, map(x-> x+1, l))+add(
`if`(l[i]>0, b(n-1, sort(subsop(i=l[i]-1, l))), 0), i=1..nops(l)))
end:
A:= (n, k)-> b(n, [0$k]):
seq(seq(A(n, d-n), n=0..d), d=0..12);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, 1, b[n - 1, l + 1] + Sum[If[l[[i]] > 0, b[n - 1, Sort[ReplacePart[l, i -> l[[i]] - 1]]], 0], {i, 1, Length[l]}]];
A[n_, k_] := b[n, Table[0, {k}]];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Jan 29 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Jan 26 2021
STATUS
approved