A192651 - OEIS

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A192651

Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+x+1. See Comments.

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

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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