A192800 Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.

0, 0, 1, 1, 4, 7, 16, 35, 73, 162, 344, 748, 1612, 3478, 7517, 16213, 35020, 75585, 163184, 352295, 760517, 1641880, 3544484, 7652008, 16519388, 35662584, 76989693, 166207785, 358815192, 774622191, 1672280660, 3610176155, 7793770037

Offset

1,5

Comments

For discussions of polynomial reduction, see A192232 and A192744.

Links

Table of n, a(n) for n=1..33.

Index entries for linear recurrences with constant coefficients, signature (1,3,0,-3,1,1).

Formula

a(n) = a(n-1)+3*a(n-2)-3*a(n-4)+a(n-5)+a(n-6).

G.f.: -x^3/(x^6+x^5-3*x^4+3*x^2+x-1). [Colin Barker, Jul 27 2012]

Example

The first five polynomials p(n,x) and their reductions:
F1(x)=1 -> 1
F2(x)=x -> x
F3(x)=x^2+1 -> x^2+1
F4(x)=x^3+2x -> x^2+2x+2
F5(x)=x^4+3x^2+1 -> 4x^2+2*x+3, so that
A192798=(1,0,1,2,3,...), A192799=(0,1,0,2,2,...), A192800=(0,0,1,1,4,...)

Mathematica

(See A192798.)

Crossrefs

Cf. A192744, A192232, A192616, A192798, A192800.

Sequence in context: A298415 A373653 A108122 * A027609 A145763 A144916

Adjacent sequences: A192797 A192798 A192799 * A192801 A192802 A192803

Keyword

nonn,easy

Author

Clark Kimberling, Jul 10 2011

Status

approved