A194010 - OEIS

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

%S 2,5,3,13,7,4,28,17,9,5,58,35,21,11,6,114,70,42,25,13,7,218,134,82,49,

%T 29,15,8,407,251,154,94,56,33,17,9,747,461,284,174,106,63,37,19,10,

%U 1352,835,515,317,194,118,70,41,21,11,2420,1495,923,569,350,214

%N Mirror of the triangle A194009.

%C A194010 is obtained by reversing the rows of the triangle A194009.

%F Write w(n,k) for the triangle at A194009.  The triangle at A194010 is then given by w(n,n-k).

%e First six rows:

%e 2

%e 5.....3

%e 13....7....4

%e 28....17...9....5

%e 58....35...21...11...6

%e 114...70...42...25...13...7

%t z = 11;

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

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

%t p1[n_, k_] := Coefficient[p[n, x], x^k];

%t p1[n_, 0] := p[n, x] /. x -> 0;

%t d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]

%t h[n_] := CoefficientList[d[n, x], {x}]

%t TableForm[Table[Reverse[h[n]], {n, 0, z}]]

%t Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A194009 *)

%t TableForm[Table[h[n], {n, 0, z}]]

%t Flatten[Table[h[n], {n, -1, z}]]  (* A194010 *)

%Y Cf. A194009.

%K nonn,tabl

%O 0,1

%A _Clark Kimberling_, Aug 11 2011