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A192800 Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.

%I A192800 #13 Feb 18 2025 12:18:57
%S A192800 0,0,1,1,4,7,16,35,73,162,344,748,1612,3478,7517,16213,35020,75585,
%T A192800 163184,352295,760517,1641880,3544484,7652008,16519388,35662584,
%U A192800 76989693,166207785,358815192,774622191,1672280660,3610176155,7793770037
%N A192800 Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.
%C A192800 For discussions of polynomial reduction, see A192232 and A192744.
%H A192800 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,0,-3,1,1).
%F A192800 a(n) = a(n-1)+3*a(n-2)-3*a(n-4)+a(n-5)+a(n-6).
%F A192800 G.f.: -x^3/(x^6+x^5-3*x^4+3*x^2+x-1). [_Colin Barker_, Jul 27 2012]
%e A192800 The first five polynomials p(n,x) and their reductions:
%e A192800 F1(x)=1 -> 1
%e A192800 F2(x)=x -> x
%e A192800 F3(x)=x^2+1 -> x^2+1
%e A192800 F4(x)=x^3+2x -> x^2+2x+2
%e A192800 F5(x)=x^4+3x^2+1 -> 4x^2+2*x+3, so that
%e A192800 A192798=(1,0,1,2,3,...), A192799=(0,1,0,2,2,...), A192800=(0,0,1,1,4,...)
%t A192800 (See A192798.)
%Y A192800 Cf. A192744, A192232, A192616, A192798, A192800.
%K A192800 nonn,easy
%O A192800 1,5
%A A192800 _Clark Kimberling_, Jul 10 2011