A194008 Mirror of the triangle A194007.

1, 5, 2, 14, 8, 3, 34, 23, 13, 5, 74, 55, 37, 21, 8, 152, 120, 89, 60, 34, 13, 299, 246, 194, 144, 97, 55, 21, 571, 484, 398, 314, 233, 157, 89, 34, 1066, 924, 783, 644, 508, 377, 254, 144, 55, 1956, 1725, 1495, 1267, 1042, 822, 610, 411, 233, 89, 3540

Offset: 0

Author

Clark Kimberling, Aug 11 2011

Keywords

• nonn
• tabl

Comments

A194008 is obtained by reversing the rows of the triangle A194007.

Examples

			First six rows:
1
5....2
14...8....3
34...23...13...5
74...55...37...21...8
152..120..89...60...34...13
		

Crossrefs

Cf. A194007.

Programs

Mathematica

z = 11;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := x*q[n - 1, x] + n + 1; q[0, n_] := 1;
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x -> 0;
d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A194007 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A194008 *)

Formula

Write w(n,k) for the triangle at A194007. The triangle at A194008 is then given by w(n,n-k).