login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192651 Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+x+1.  See Comments. 3
0, 0, 1, 1, 5, 8, 23, 47, 113, 252, 578, 1316, 2994, 6832, 15545, 35445, 80711, 183928, 418973, 954571, 2174681, 4954436, 11287336, 25715016, 58584744, 133468980, 304072713, 692745597, 1578230845, 3595564360, 8191505015, 18662090915 (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..32.

Index entries for linear recurrences with constant coefficients, signature (1,4,-1,-4,1,1).

FORMULA

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

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

EXAMPLE

The first five polynomials p(n,x) and their reductions are as follows:

F1(x)=1 -> 1

F2(x)=x -> x

F3(x)=x^2+1 -> x^2+1

F4(x)=x^3+2x -> x^2+3x+1

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

A192616=(1,0,1,1,2,...), A192617=(0,1,0,3,2,...), A192651=(0,0,1,1,5,...)

MATHEMATICA

(See A192616.)

CROSSREFS

Cf. A192232, A192744, A192616.

Sequence in context: A063897 A092733 A116884 * A105963 A270125 A264797

Adjacent sequences:  A192648 A192649 A192650 * A192652 A192653 A192654

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 09 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 16:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)