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A193907 Mirror of the triangle A193906. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A199468 A004732 A160641

Adjacent sequences:  A193904 A193905 A193906 * A193908 A193909 A193910

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 08 2011

STATUS

approved

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Last modified December 11 03:07 EST 2016. Contains 279034 sequences.