OFFSET
0,3
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(n,k) = Sum_{j=0..n} binomial(n-j,k*j).
A(n,k) = A306713(k*n,k) for k > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, ...
3, 2, 1, 1, 1, 1, 1, 1, 1, ...
4, 3, 2, 1, 1, 1, 1, 1, 1, ...
5, 5, 4, 2, 1, 1, 1, 1, 1, ...
6, 8, 7, 5, 2, 1, 1, 1, 1, ...
7, 13, 12, 11, 6, 2, 1, 1, 1, ...
8, 21, 21, 21, 16, 7, 2, 1, 1, ...
9, 34, 37, 37, 36, 22, 8, 2, 1, ...
MATHEMATICA
T[n_, k_] := Sum[Binomial[n - j, k*j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 21 2021 *)
CROSSREFS
AUTHOR
Seiichi Manyama, Mar 05 2019
STATUS
approved