A193957 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}.

1, 1, 1, 2, 3, 5, 3, 5, 9, 14, 4, 7, 13, 21, 34, 5, 9, 17, 28, 46, 74, 6, 11, 21, 35, 58, 94, 152, 7, 13, 25, 42, 70, 114, 185, 299, 8, 15, 29, 49, 82, 134, 218, 353, 571, 9, 17, 33, 56, 94, 154, 251, 407, 659, 1066, 10, 19, 37, 63, 106, 174, 284, 461, 747, 1209

Offset

0,4

Comments

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

Links

Table of n, a(n) for n=0..64.

Example

First six rows:
1
1...1
2...3...5
3...5...9....14
4...7...13...21...34
5...9...17...28...46...74

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. A193722, A193958.

Sequence in context: A261324 A224887 A151571 * A336746 A209769 A114230

Adjacent sequences: A193954 A193955 A193956 * A193958 A193959 A193960

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved