A194010 Mirror of the triangle A194009.

2, 5, 3, 13, 7, 4, 28, 17, 9, 5, 58, 35, 21, 11, 6, 114, 70, 42, 25, 13, 7, 218, 134, 82, 49, 29, 15, 8, 407, 251, 154, 94, 56, 33, 17, 9, 747, 461, 284, 174, 106, 63, 37, 19, 10, 1352, 835, 515, 317, 194, 118, 70, 41, 21, 11, 2420, 1495, 923, 569, 350, 214

Offset: 0

Author

Clark Kimberling, Aug 11 2011

Keywords

• nonn
• tabl

Comments

A194010 is obtained by reversing the rows of the triangle A194009.

Examples

			First six rows:
2
5.....3
13....7....4
28....17...9....5
58....35...21...11...6
114...70...42...25...13...7
		

Crossrefs

Cf. A194009.

Programs

Mathematica

z = 11;
p[n_, x_] := x*p[n - 1, x] + n + 1; p[0, n_] := 1;
q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
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}]]  (* A194009 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A194010 *)

Formula

Write w(n,k) for the triangle at A194009. The triangle at A194010 is then given by w(n,n-k).