A193907 Mirror of the triangle A193906.

1, 2, 1, 8, 5, 2, 23, 14, 8, 3, 63, 39, 23, 13, 5, 167, 103, 63, 37, 21, 8, 440, 272, 167, 102, 60, 34, 13, 1154, 713, 440, 270, 165, 97, 55, 21, 3024, 1869, 1154, 712, 437, 267, 157, 89, 34, 7919, 4894, 3024, 1867, 1152, 707, 432, 254, 144, 55, 20735, 12815

Offset

0,2

Comments

A193907 is obtained by reversing the rows of the triangle A193906.

Links

Table of n, a(n) for n=0..56.

Formula

Write w(n,k) for the triangle at A193906. The triangle at A193907 is then given by w(n,n-k).

Example

First six rows:
1
2....1
8....5....2
23...14...8....3
63...39...23...13...5
167..103..63...37...21...8

Mathematica

z = 12;
p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];
q[n_, x_] := p[n, x]
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}]]  (* A193906 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193907 *)

Crossrefs

Cf. A193906.

Sequence in context: A135520 A136230 A193892 * A298592 A344163 A199468

Adjacent sequences: A193904 A193905 A193906 * A193908 A193909 A193910

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved