A193924 Mirror of the triangle A193923.

1, 1, 1, 3, 2, 1, 8, 5, 3, 1, 21, 13, 8, 4, 1, 55, 34, 21, 12, 5, 1, 144, 89, 55, 33, 17, 6, 1, 377, 233, 144, 88, 50, 23, 7, 1, 987, 610, 377, 232, 138, 73, 30, 8, 1, 2584, 1597, 987, 609, 370, 211, 103, 38, 9, 1, 6765, 4181, 2584, 1596, 979, 581, 314, 141, 47

Offset

0,4

Comments

A193924 is obtained by reversing the rows of the triangle A193923.

Links

Table of n, a(n) for n=0..63.

Formula

Write w(n,k) for the triangle at A193923. The triangle at A193924 is then given by w(n,n-k).

Example

First six rows:
1
1....1
3....2....1
8....5....3....1
21...13...8....4....1
55...34...21...12...5...1

Mathematica

p[n_, x_] := (x + 1)^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}]]  (* A193923 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193924 *)

Crossrefs

Cf. A193923.

Sequence in context: A090452 A305538 A370527 * A110439 A327917 A065602

Adjacent sequences: A193921 A193922 A193923 * A193925 A193926 A193927

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 09 2011

Status

approved