A193909 - OEIS

%I #5 Mar 30 2012 18:57:39

%S 1,1,2,3,6,8,6,12,20,24,11,22,40,64,80,19,38,72,128,208,256,32,64,124,

%T 232,416,672,832,53,106,208,400,752,1344,2176,2688,87,174,344,672,

%U 1296,2432,4352,7040,8704,142,284,564,1112,2176,4192,7872,14080,22784

%N Mirror of the triangle A193908.

%C A193909 is obtained by reversing the rows of the triangle A193908.

%F Write w(n,k) for the triangle at A193908.  The triangle at A193909 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....2

%e 3....6....8

%e 6....12...20...24

%e 11...22...40...64....80

%e 19...38...72...128...208...256

%t z = 12;

%t p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];

%t q[n_, x_] := 2 x*q[n - 1, x] + 1 ; q[0, x_] := 1;

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193908 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193909 *)

%Y Cf. A193908.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 09 2011