A193958 Mirror of the triangle A193955.

1, 1, 1, 5, 3, 2, 14, 9, 5, 3, 34, 21, 13, 7, 4, 74, 46, 28, 17, 9, 5, 152, 94, 58, 35, 21, 11, 6, 299, 185, 114, 70, 42, 25, 13, 7, 571, 353, 218, 134, 82, 49, 29, 15, 8, 1066, 659, 407, 251, 154, 94, 56, 33, 17, 9, 1956, 1209, 747, 461, 284, 174, 106, 63, 37

Offset

0,4

Comments

A193958 is obtained by reversing the rows of the triangle A193957.

Links

Table of n, a(n) for n=0..63.

Formula

Write w(n,k) for the triangle at A193957. The triangle at A193958 is then given by w(n,n-k).

Example

First six rows:
1
1....1
5....3....1
14...9....5...3
34...21...13..7...4
74...46...28..17..9..5

Mathematica

z = 12;
p[n_, x_] := x*p[n - 1, x] + n + 1; p[0, x_] := 1 ;
q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193957 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193958 *)

Crossrefs

Cf. A193957.

Sequence in context: A309276 A268690 A065627 * A322289 A259228 A241182

Adjacent sequences: A193955 A193956 A193957 * A193959 A193960 A193961

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved