login
Mirror of the triangle A193955.
2

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

%S 1,4,1,13,5,1,45,23,9,2,120,71,36,14,3,300,196,116,59,23,5,692,484,

%T 316,187,95,37,8,1524,1121,784,512,303,154,60,13,3225,2465,1813,1268,

%U 828,490,249,97,21,6625,5219,3989,2934,2052,1340,793,403,157,34,13280

%N Mirror of the triangle A193955.

%C A193956 is obtained by reversing the rows of the triangle A193955.

%F Write w(n,k) for the triangle at A193955. The triangle at A193955 is then given by w(n,n-k).

%e First six rows:

%e 1

%e 4.....1

%e 13....5....1

%e 45....23...9....2

%e 120...71...36...14..3

%e 300...192..116..59..23..5

%t z = 12;

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

%t q[n_, x_] := Sum[((k + 1)^2)*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}]] (* A193955 *)

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

%t Flatten[Table[g[n], {n, -1, z}]] (* A193956 *)

%Y Cf. A193955.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_, Aug 10 2011