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 A193916 Mirror of the triangle A193915. 2

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

%S 1,1,2,2,4,4,4,8,12,16,7,14,24,40,48,12,24,44,80,128,160,20,40,76,144,

%T 256,416,512,33,66,128,248,464,832,1344,1664,54,108,212,416,800,1504,

%U 2688,4352,5376,88,176,348,688,1344,2592,4864,8704,14080,17408

%N Mirror of the triangle A193915.

%C A193916 is obtained by reversing the rows of the triangle A193915.

%F Write w(n,k) for the triangle at A193915. The triangle at A193916 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....2

%e 2....4....4

%e 4....8....12...16

%e 7....14...24...40...48

%e 12...24...44...80...128...160

%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. A193915, A193909.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 09 2011

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Last modified March 1 05:26 EST 2024. Contains 370430 sequences. (Running on oeis4.)