A194009 Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).

2, 3, 5, 4, 7, 13, 5, 9, 17, 28, 6, 11, 21, 35, 58, 7, 13, 25, 42, 70, 114, 8, 15, 29, 49, 82, 134, 218, 9, 17, 33, 56, 94, 154, 251, 407, 10, 19, 37, 63, 106, 174, 284, 461, 747, 11, 21, 41, 70, 118, 194, 317, 515, 835, 1352, 12, 23, 45, 77, 130, 214, 350, 569

Offset

0,1

Comments

See A193842 for the definition of the fission of P by Q, where P and Q are sequences of polynomials or triangular arrays (of coefficients of polynomials).

Links

Table of n, a(n) for n=0..62.

Example

First six rows:
2
3...5
4...7....13
5...9....17...28
6...11...21...35...58
7...13...25...42...70...114

Mathematica

z = 11;
p[n_, x_] := x*p[n - 1, x] + n + 1; p[0, n_] := 1;
q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, 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}]]  (* A194009 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, -1, z}]]  (* A194010 *)

Crossrefs

Cf. A193842, A194010.

Sequence in context: A355066 A028691 A246353 * A242388 A257985 A089557

Adjacent sequences: A194006 A194007 A194008 * A194010 A194011 A194012

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 11 2011

Status

approved