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A192799 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.

%I A192799 #14 Feb 18 2025 12:37:57
%S A192799 0,1,0,2,2,5,12,22,54,109,242,520,1118,2427,5218,11290,24352,52579,
%T A192799 113526,245038,529068,1142087,2465644,5322896,11491188,24807721,
%U A192799 53555508,115617714,249599214,538843277,1163273304,2511313222,5421508714
%N A192799 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.
%C A192799 For discussions of polynomial reduction, see A192232 and A192744.
%H A192799 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,0,-3,1,1).
%F A192799 a(n) = a(n-1)+3*a(n-2)-3*a(n-4)+a(n-5)+a(n-6).
%F A192799 G.f.: x^2*(x^2+x-1)/(x^6+x^5-3*x^4+3*x^2+x-1). [_Colin Barker_, Jul 27 2012]
%e A192799 The first five polynomials p(n,x) and their reductions:
%e A192799 F1(x)=1 -> 1
%e A192799 F2(x)=x -> x
%e A192799 F3(x)=x^2+1 -> x^2+1
%e A192799 F4(x)=x^3+2x -> x^2+2x+2
%e A192799 F5(x)=x^4+3x^2+1 -> 4x^2+2*x+3, so that
%e A192799 A192798=(1,0,1,2,3,...), A192799=(0,1,0,2,2,...), A192800=(0,0,1,1,4,...)
%t A192799 (See A192798.)
%Y A192799 Cf. A192232, A192744, A192798.
%K A192799 nonn,easy
%O A192799 1,4
%A A192799 _Clark Kimberling_, Jul 10 2011