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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
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 (list; table; graph; refs; listen; history; text; internal format)
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: A259153 A028691 A246353 * A242388 A257985 A089557

Adjacent sequences:  A194006 A194007 A194008 * A194010 A194011 A194012

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 11 2011

STATUS

approved

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Last modified March 20 05:17 EDT 2019. Contains 321344 sequences. (Running on oeis4.)