A193909 Mirror of the triangle A193908.

1, 1, 2, 3, 6, 8, 6, 12, 20, 24, 11, 22, 40, 64, 80, 19, 38, 72, 128, 208, 256, 32, 64, 124, 232, 416, 672, 832, 53, 106, 208, 400, 752, 1344, 2176, 2688, 87, 174, 344, 672, 1296, 2432, 4352, 7040, 8704, 142, 284, 564, 1112, 2176, 4192, 7872, 14080, 22784

Offset

0,3

Comments

A193909 is obtained by reversing the rows of the triangle A193908.

Links

Table of n, a(n) for n=0..53.

Formula

Write w(n,k) for the triangle at A193908. The triangle at A193909 is then given by w(n,n-k).

Example

First six rows:
1
1....2
3....6....8
6....12...20...24
11...22...40...64....80
19...38...72...128...208...256

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. A193908.

Sequence in context: A246266 A284385 A282940 * A211603 A221956 A249549

Adjacent sequences: A193906 A193907 A193908 * A193910 A193911 A193912

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 09 2011

Status

approved