login
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
OFFSET
1,5
COMMENTS
For discussions of polynomial reduction, see A192232 and A192744.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved