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

0,3

Comments

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

Links

Table of n, a(n) for n=0..54.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A193915, A193909.

Sequence in context: A306060 A317238 A260038 * A304347 A316218 A305642

Adjacent sequences: A193913 A193914 A193915 * A193917 A193918 A193919

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 09 2011

Status

approved