A193954 Mirror of the triangle A193953.

1, 2, 1, 5, 3, 1, 13, 9, 5, 2, 28, 21, 14, 8, 3, 58, 46, 34, 23, 13, 5, 114, 94, 74, 55, 37, 21, 8, 218, 185, 152, 120, 89, 60, 34, 13, 407, 353, 299, 246, 194, 144, 97, 55, 21, 747, 659, 571, 484, 398, 314, 233, 157, 89, 34, 1352, 1209, 1066, 924, 783, 644

Offset

0,2

Comments

A193954 is obtained by reversing the rows of the triangle A193953.

Links

Table of n, a(n) for n=0..60.

Formula

Write w(n,k) for the triangle at A193953. The triangle at A193954 is then given by w(n,n-k).

Example

First six rows:
1
2....1
5....3....1
13...9....5....2
28...21...14...8...3
58...46...34...23..13..5

Mathematica

z = 12;
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, x_] := 1
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}]]  (* A193953 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193954 *)

Crossrefs

Cf. A193953.

Sequence in context: A280784 A048472 A038622 * A162997 A112339 A132808

Adjacent sequences: A193951 A193952 A193953 * A193955 A193956 A193957

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved