A192799 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.

0, 1, 0, 2, 2, 5, 12, 22, 54, 109, 242, 520, 1118, 2427, 5218, 11290, 24352, 52579, 113526, 245038, 529068, 1142087, 2465644, 5322896, 11491188, 24807721, 53555508, 115617714, 249599214, 538843277, 1163273304, 2511313222, 5421508714

Offset

1,4

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^2*(x^2+x-1)/(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. A192232, A192744, A192798.

Sequence in context: A233357 A248664 A143195 * A181354 A384069 A085289

Adjacent sequences: A192796 A192797 A192798 * A192800 A192801 A192802

Keyword

nonn,easy

Author

Clark Kimberling, Jul 10 2011

Status

approved