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%I #9 Jun 13 2015 00:53:54
%S 0,0,1,1,4,6,14,26,52,103,201,400,784,1552,3056,6032,11897,23465,
%T 46292,91302,180110,355258,700772,1382287,2726609,5378336,10608928,
%U 20926496,41278176,81422624,160608817,316806289,624911012,1232657862,2431458958
%N Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1.
%C For discussions of polynomial reduction, see A192232 and A192744.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1,-3,1,1).
%F a(n)=a(n-1)+3*a(n-2)-a(n-3)-3*a(n-4)+a(n-5)+a(n-6).
%F G.f.: -x^3/(x^6+x^5-3*x^4-x^3+3*x^2+x-1). [_Colin Barker_, Nov 23 2012]
%e The first five polynomials p(n,x) and their reductions:
%e F1(x)=1 -> 1
%e F2(x)=x -> x
%e F3(x)=x^2+1 -> x^2+1
%e F4(x)=x^3+2x -> x^2+2x+1
%e F5(x)=x^4+3x^2+1 -> 4x^2+1x+2, so that
%e A192777=(1,0,1,1,2,...), A192778=(0,1,0,2,1,...), A192779=(0,0,1,1,4,...)
%t (See A192780.)
%Y Cf. A192744, A192232, A192616, A192780, A192781.
%K nonn,easy
%O 1,5
%A _Clark Kimberling_, Jul 09 2011
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