A193950 Mirror of the triangle A193949.

1, 4, 2, 13, 8, 3, 45, 32, 19, 8, 120, 92, 64, 38, 15, 300, 242, 184, 128, 75, 30, 692, 578, 464, 352, 243, 142, 56, 1524, 1306, 1088, 872, 659, 454, 264, 104, 3225, 2818, 2411, 2006, 1604, 1210, 831, 482, 189, 6625, 5878, 5131, 4386, 3644, 2910, 2191

Offset

0,2

Comments

A193950 is obtained by reversing the rows of the triangle A193949.

Links

Table of n, a(n) for n=0..51.

Formula

Write w(n,k) for the triangle at A193949. The triangle at A193950 is then given by w(n,n-k).

Example

First six rows:
1
4.....2
13....8.....3
45....32....19....8
120...92....64....38....15
300...242...184...128...75...30

Mathematica

z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[(k + 1) (n + 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}]]  (* A193949 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193950 *)

Crossrefs

Cf. A193949.

Sequence in context: A224820 A125153 A191451 * A180194 A193853 A213853

Adjacent sequences: A193947 A193948 A193949 * A193951 A193952 A193953

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved