A193998 Mirror of the triangle A193997.

1, 3, 2, 6, 8, 3, 11, 23, 18, 5, 19, 55, 66, 37, 8, 32, 120, 196, 167, 73, 13, 53, 246, 511, 587, 388, 139, 21, 87, 484, 1225, 1777, 1578, 853, 259, 34, 142, 924, 2765, 4857, 5428, 3933, 1799, 474, 55, 231, 1725, 5969, 12333, 16642, 15147, 9275, 3678

Offset

0,2

Comments

A193998 is obtained by reversing the rows of the triangle A193997.

Links

Table of n, a(n) for n=0..52.

Formula

Write w(n,k) for the triangle at A193997. The triangle at A193998 is then given by w(n,n-k).

Example

First six rows:
1
3....2
6....8.....3
11...23....18....5
19...55....66....37....8
32...120...196...167...73...13

Mathematica

z = 11;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := (x + 1)^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}]]  (* A193997 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A193998 *)

Crossrefs

Cf. A193997.

Sequence in context: A370665 A127717 A210236 * A209171 A368150 A348686

Adjacent sequences: A193995 A193996 A193997 * A193999 A194000 A194001

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 11 2011

Status

approved