%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