A193952 Mirror of the triangle A193951.

1, 1, 1, 10, 6, 4, 42, 27, 15, 9, 136, 84, 52, 28, 16, 370, 230, 140, 85, 45, 25, 912, 564, 348, 210, 126, 66, 36, 2093, 1295, 798, 490, 294, 175, 91, 49, 4568, 2824, 1744, 1072, 656, 392, 232, 120, 64, 9594, 5931, 3663, 2259, 1386, 846, 504, 297, 153

Offset

0,4

Comments

A193952 is obtained by reversing the rows of the triangle A193951.

Links

Table of n, a(n) for n=0..53.

Formula

Write w(n,k) for the triangle at A193951. The triangle at A193952 is then given by w(n,n-k).

Example

First six rows:
1
1.....1
10....6....4
42....27...15...9
136...84...52...28..16
370...230..140..85..45..25

Mathematica

z = 12;
p[n_, x_] := Sum[(k + 1) (n + 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}]]  (* A193951 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193952 *)

Crossrefs

Cf. A193952.

Sequence in context: A010171 A006518 A094175 * A158508 A102690 A076366

Adjacent sequences: A193949 A193950 A193951 * A193953 A193954 A193955

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved