A193921 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)=x^n+x^(n-1)+...+x+1.

1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 3, 5, 6, 7, 7, 5, 8, 10, 11, 12, 12, 8, 13, 16, 18, 19, 20, 20, 13, 21, 26, 29, 31, 32, 33, 33, 21, 34, 42, 47, 50, 52, 53, 54, 54, 34, 55, 68, 76, 81, 84, 86, 87, 88, 88, 55, 89, 110, 123, 131, 136, 139, 141, 142, 143, 143, 89, 144, 178

Offset

0,5

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..68.

Example

First six rows:
1
1...1
1...2...2
2...3...4....4
3...5...6....7....7
5...8...10...11...12...12

Mathematica

p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := x*q[n - 1, x] + 1; q[0, n_] := 1;
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}]]  (* A193921 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193922 *)

Crossrefs

Cf. A193722, A193922.

Sequence in context: A300401 A051601 A296612 * A074829 A060243 A054225

Adjacent sequences: A193918 A193919 A193920 * A193922 A193923 A193924

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 09 2011

Status

approved