A194008 Mirror of the triangle A194007.

1, 5, 2, 14, 8, 3, 34, 23, 13, 5, 74, 55, 37, 21, 8, 152, 120, 89, 60, 34, 13, 299, 246, 194, 144, 97, 55, 21, 571, 484, 398, 314, 233, 157, 89, 34, 1066, 924, 783, 644, 508, 377, 254, 144, 55, 1956, 1725, 1495, 1267, 1042, 822, 610, 411, 233, 89, 3540

Offset

0,2

Comments

A194008 is obtained by reversing the rows of the triangle A194007.

Links

Table of n, a(n) for n=0..55.

Formula

Write w(n,k) for the triangle at A194007. The triangle at A194008 is then given by w(n,n-k).

Example

First six rows:
1
5....2
14...8....3
34...23...13...5
74...55...37...21...8
152..120..89...60...34...13

Mathematica

z = 11;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := x*q[n - 1, x] + n + 1; q[0, n_] := 1;
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A194007 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A194008 *)

Crossrefs

Cf. A194007.

Sequence in context: A194048 A158868 A104634 * A060422 A213751 A185781

Adjacent sequences: A194005 A194006 A194007 * A194009 A194010 A194011

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 11 2011

Status

approved