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A194008 Mirror of the triangle A194007. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 2 09:56 EST 2021. Contains 341746 sequences. (Running on oeis4.)