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Mirror of the triangle A193969.
2

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

%S 1,3,1,7,4,1,21,12,7,2,54,33,19,11,3,144,88,54,31,18,5,376,232,142,87,

%T 50,29,8,987,609,376,230,141,81,47,13,2583,1596,985,608,372,228,131,

%U 76,21,6765,4180,2583,1594,984,602,369,212,123,34,17710,10945,6763

%N Mirror of the triangle A193969.

%C A193969 is obtained by reversing the rows of the triangle A193970.

%F Write w(n,k) for the triangle at A193969. The triangle at A193970 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 3....1

%e 7....4....1

%e 21...12...7....2

%e 54...33...19...11...3

%e 144..88...54...31...18...5

%t z = 12;

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

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

%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}]] (* A193969 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193970 *)

%Y Cf. A193969.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011