A193968 - OEIS

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

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

%T 87,54,29,18,985,609,376,232,141,87,47,29,2583,1596,987,608,376,228,

%U 141,76,47,6763,4180,2583,1596,984,608,369,228,123,76,17710,10945

%N Mirror of the triangle A193967.

%C A193967 is obtained by reversing the rows of the triangle A193968.

%F Write w(n,k) for the triangle at A193967.  The triangle at A193968 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 1....1

%e 7....4....3

%e 19...12...7...4

%e 54...33...21..11..7

%e 142..88...54..33..18..11

%t z = 12;

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

%t q[n_, x_] := Sum[Fibonacci[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}]]  (* A193967 *)

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

%t Flatten[Table[g[n], {n, -1, z}]]  (* A193968 *)

%Y Cf. A193968.

%K nonn,tabl

%O 0,4

%A _Clark Kimberling_, Aug 10 2011