A193960 Mirror of the triangle A193959.

1, 1, 1, 9, 5, 4, 36, 23, 13, 9, 116, 71, 45, 25, 16, 316, 196, 120, 75, 41, 25, 784, 484, 300, 183, 113, 61, 36, 1813, 1121, 692, 428, 260, 159, 85, 49, 3989, 2465, 1524, 940, 580, 351, 213, 113, 64, 8444, 5219, 3225, 1993, 1228, 756, 456, 275, 145, 81

Offset

0,4

Comments

A193960 is obtained by reversing the rows of the triangle A193959.

Links

Table of n, a(n) for n=0..54.

Formula

Write w(n,k) for the triangle at A193959. The triangle at A193960 is then given by w(n,n-k).

Example

First six rows:
1
1.....1
9.....5....4
36....23...13...9
116...71...45...25..16
316...196..120..75..41..25

Mathematica

z = 12;
p[n_, x_] := Sum[((k + 1)^2)*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}]]  (* A193959 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193960 *)

Crossrefs

Cf. A193959.

Sequence in context: A259148 A089491 A199792 * A377522 A195696 A362000

Adjacent sequences: A193957 A193958 A193959 * A193961 A193962 A193963

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved