

A192773


Coefficient of x in the reduction of the nth Fibonacci polynomial by x^3>x^2+2x+1.


3



0, 1, 0, 4, 3, 18, 30, 98, 219, 596, 1464, 3783, 9540, 24328, 61740, 156985, 398904, 1013772, 2576475, 6547574, 16640382, 42288806, 107473443, 273129468, 694130016, 1764047839, 4483130424, 11393354512, 28954911624, 73585574049
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


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(n1)+5*a(n2)a(n3)5*a(n4)+a(n5)+a(n6).
G.f.: x^2*(x^2+x1)/(x^6+x^55*x^4x^3+5*x^2+x1). [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.)


CROSSREFS

Cf. A192232, A192744, A192772.
Sequence in context: A302851 A276083 A161893 * A183231 A241358 A178417
Adjacent sequences: A192770 A192771 A192772 * A192774 A192775 A192776


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 09 2011


STATUS

approved



