A193916 Mirror of the triangle A193915.

1, 1, 2, 2, 4, 4, 4, 8, 12, 16, 7, 14, 24, 40, 48, 12, 24, 44, 80, 128, 160, 20, 40, 76, 144, 256, 416, 512, 33, 66, 128, 248, 464, 832, 1344, 1664, 54, 108, 212, 416, 800, 1504, 2688, 4352, 5376, 88, 176, 348, 688, 1344, 2592, 4864, 8704, 14080, 17408

Offset: 0

Author

Clark Kimberling, Aug 09 2011

Keywords

• nonn
• tabl

Comments

A193916 is obtained by reversing the rows of the triangle A193915.

Examples

			First six rows:
1
1....2
2....4....4
4....8....12...16
7....14...24...40...48
12...24...44...80...128...160
		

Crossrefs

Cf. A193915, A193909.

Programs

Mathematica

z = 12;
p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];
q[n_, x_] := 2 x*q[n - 1, x] + 1 ; q[0, x_] := 1;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193908 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193909 *)

Formula

Write w(n,k) for the triangle at A193915. The triangle at A193916 is then given by w(n,n-k).