cp's OEIS Frontend

A192778 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.

%I A192778 #13 Feb 18 2025 12:37:13
%S A192778 0,1,0,5,4,28,48,183,424,1315,3420,9864,26756,75237,207128,577345,
%T A192778 1597624,4439764,12307388,34166643,94769936,262998791,729644824,
%U A192778 2024614928,5617339496,15586328073,43245649904,119991232893,332929027020
%N A192778 Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.
%C A192778 For discussions of polynomial reduction, see A192232 and A192744.
%H A192778 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-1,-6,1,1).
%F A192778 a(n) = a(n-1)+6*a(n-2)-a(n-3)-6*a(n-4)+a(n-5)+a(n-6).
%F A192778 G.f.: x^2*(x^2+x-1)/((x^2-x-1)*(x^4+2*x^3-3*x^2-2*x+1)). [_Colin Barker_, Nov 23 2012]
%e A192778 The first five polynomials p(n,x) and their reductions:
%e A192778 F1(x)=1 -> 1
%e A192778 F2(x)=x -> x
%e A192778 F3(x)=x^2+1 -> x^2+1
%e A192778 F4(x)=x^3+2x -> x^2+5x+1
%e A192778 F5(x)=x^4+3x^2+1 -> 7x^2+4x+2, so that
%e A192778 A192777=(1,0,1,1,2,...), A192778=(0,1,0,5,4,...), A192779=(0,0,1,1,7,...)
%Y A192778 Cf. A192744, A192232, A192616, A192772, A192777, A192779.
%K A192778 nonn,easy
%O A192778 1,4
%A A192778 _Clark Kimberling_, Jul 09 2011