A193968 Mirror of the triangle A193967.

1, 1, 1, 7, 4, 3, 19, 12, 7, 4, 54, 33, 21, 11, 7, 142, 88, 54, 33, 18, 11, 376, 232, 144, 87, 54, 29, 18, 985, 609, 376, 232, 141, 87, 47, 29, 2583, 1596, 987, 608, 376, 228, 141, 76, 47, 6763, 4180, 2583, 1596, 984, 608, 369, 228, 123, 76, 17710, 10945

Offset

0,4

Comments

A193967 is obtained by reversing the rows of the triangle A193968.

Links

Table of n, a(n) for n=0..56.

Formula

Write w(n,k) for the triangle at A193967. The triangle at A193968 is then given by w(n,n-k).

Example

First six rows:
1
1....1
7....4....3
19...12...7...4
54...33...21..11..7
142..88...54..33..18..11

Mathematica

z = 12;
p[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
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}]]  (* A193967 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193968 *)

Crossrefs

Cf. A193968.

Sequence in context: A065477 A272526 A100041 * A153840 A198351 A354249

Adjacent sequences: A193965 A193966 A193967 * A193969 A193970 A193971

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved