A192774 Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2x+1.

0, 0, 1, 1, 6, 10, 34, 74, 206, 499, 1301, 3264, 8348, 21152, 53828, 136720, 347533, 883157, 2244462, 5704094, 14496130, 36840606, 93625542, 237939591, 604694601, 1536764208, 3905506648, 9925401280, 25224262440, 64104575344

Offset

1,5

Comments

For discussions of polynomial reduction, see A192232 and A192744.

Links

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (1,5,-1,-5,1,1).

Formula

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

G.f.: -x^3/(x^6+x^5-5*x^4-x^3+5*x^2+x-1). [Colin Barker, Nov 23 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+4x+1
F5(x)=x^4+3x^2+1 -> 6x^2+3x+2, so that
A192772=(1,0,1,1,2,...), A192773=(0,1,0,4,3,...), A192774=(0,0,1,1,6,...)

Mathematica

(See A192772.)
LinearRecurrence[{1, 5, -1, -5, 1, 1}, {0, 0, 1, 1, 6, 10}, 30] (* Harvey P. Dale, Jun 25 2017 *)

Crossrefs

Cf. A192232, A192744, A192772.

Sequence in context: A137272 A121801 A256721 * A218860 A242866 A360519

Adjacent sequences: A192771 A192772 A192773 * A192775 A192776 A192777

Keyword

nonn,easy

Author

Clark Kimberling, Jul 09 2011

Status

approved