A192782 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1.

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

Offset: 1

Author

Clark Kimberling, Jul 09 2011

Keywords

• nonn
• easy

Comments

For discussions of polynomial reduction, see A192232 and A192744.

Examples

			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,...)
		

Links

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

Crossrefs

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

Programs

Mathematica

(See A192780.)

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]