A274200 Limiting reverse row of the array A274193.

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 20, 27, 35, 45, 60, 77, 101, 132, 170, 223, 289, 375, 490, 634, 826, 1074, 1392, 1813, 2352, 3055, 3973, 5154, 6700, 8702, 11296, 14681, 19058, 24754, 32156, 41747, 54232, 70425, 91451, 118786, 154241, 200319, 260157

Offset: 1

Author

Clark Kimberling, Jun 16 2016

Keywords

• nonn
• easy

Comments

The triangular array (g(n,k)) at A274193 is defined as follows: g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,3) for n > 0, k > 1.

Examples

			Row g(9,k):  1,4,4,4,3,2,2,1,1,1; the reversal is
1,1,1,2,2,3,4,4,4,1,..., which agrees with A274200 up to the first 7 terms.
		

Crossrefs

Cf. A274193, A274199, A274201.

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]];
z = 300; w = Reverse[Table[g[z, k], {k, 0, z}]];
Take[w, z/3]