A274193 Triangular array read by rows: g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,3k) for n > 0, k > 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 1, 1, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 4, 3, 2, 2, 1, 1, 1, 1, 5, 6, 5, 4, 3, 2, 2, 1, 1, 1, 1, 6, 7, 7, 5, 4, 3, 2, 2, 1, 1, 1, 1, 8, 9, 8, 7, 5, 4, 3

Offset: 0

Author

Clark Kimberling, Jun 14 2016

Keywords

• nonn
• tabl
• easy

Examples

			First  10 rows:
1
1   1
1   1   1
1   1   1   1
1   2   1   1   1
1   2   2   1   1   1
1   2   2   2   1   1   1
1   3   3   2   2   1   1   1
1   3   4   3   2   2   1   1   1
1   4   4   4   3   2   2   1   1   1
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A274194 (row sums), A274195, A274200 (limiting reverse row), A274190, A274196.

Programs

Mathematica

g[n_, 0] = g[n, 0] = 1;
g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 3 k]];
t = Table[g[n, k], {n, 0, 14}, {k, 0, n}]
TableForm[t] (* A274193 array *)
u = Flatten[t] (* A274193 sequence *)