

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
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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,nk).


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



