A193906 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+2)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).

1, 1, 2, 2, 5, 8, 3, 8, 14, 23, 5, 13, 23, 39, 63, 8, 21, 37, 63, 103, 167, 13, 34, 60, 102, 167, 272, 440, 21, 55, 97, 165, 270, 440, 713, 1154, 34, 89, 157, 267, 437, 712, 1154, 1869, 3024, 55, 144, 254, 432, 707, 1152, 1867, 3024, 4894, 7919, 89, 233

Offset

0,3

Comments

See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. The first five rows of P, from the coefficients of p(n,k):

1

1...2

1...2...3

1...2...3...5

1...2...3...5...8

Links

Table of n, a(n) for n=0..56.

Example

First six rows of A193906:
1
1...2
2...5....8
3...8....14...23
5...13...23...39...63
8...21...37...63...103...167

Mathematica

z = 12;
p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];
q[n_, x_] := p[n, x]
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}]]  (* A193906 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193907 *)

Crossrefs

Cf. A193722, A193907.

Sequence in context: A011021 A077232 A193891 * A224791 A210637 A201972

Adjacent sequences: A193903 A193904 A193905 * A193907 A193908 A193909

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved