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A192782 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1. 2
0, 0, 1, 1, 4, 6, 14, 26, 52, 103, 201, 400, 784, 1552, 3056, 6032, 11897, 23465, 46292, 91302, 180110, 355258, 700772, 1382287, 2726609, 5378336, 10608928, 20926496, 41278176, 81422624, 160608817, 316806289, 624911012, 1232657862, 2431458958 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

For discussions of polynomial reduction, see A192232 and A192744.

LINKS

Table of n, a(n) for n=1..35.

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

FORMULA

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

G.f.: -x^3/(x^6+x^5-3*x^4-x^3+3*x^2+x-1). [Colin Barker, Nov 23 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+1

F5(x)=x^4+3x^2+1 -> 4x^2+1x+2, so that

A192777=(1,0,1,1,2,...), A192778=(0,1,0,2,1,...), A192779=(0,0,1,1,4,...)

MATHEMATICA

(See A192780.)

CROSSREFS

Cf. A192744, A192232, A192616, A192780, A192781.

Sequence in context: A027632 A175722 A200186 * A306742 A188576 A084214

Adjacent sequences:  A192779 A192780 A192781 * A192783 A192784 A192785

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 09 2011

STATUS

approved

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Last modified June 12 14:20 EDT 2021. Contains 344956 sequences. (Running on oeis4.)