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A231184 Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.

%I A231184 #8 Apr 26 2019 11:17:30
%S A231184 -1,0,0,3,6,17,32,73,135,286,528,1080,2002,4015,7485,14827,27796,
%T A231184 54606,102869,200909,380006,739013,1402309,2718485,5171573,10001553,
%U A231184 19064476,36802823,70259834,135444612,258883604,498538557,953762458
%N A231184 Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.
%C A231184 The formula for rho(11)^n is (see A231182): rho(11)^n = A231182(n)*1 - A231183(n)*rho(11) - a(n-2)*rho(11)^2 + A231185(n-3)*rho(11)^3 + A231182(n+1)*rho(11)^4, n >= 0.
%H A231184 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-3,1).
%F A231184 G.f.: (-1 + x + 4*x^2)/(1-x-4*x^2+3*x^3+3*x^4-x^5).
%F A231184 a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 3, with a(-2)=a(-1)=0 , a(0)=-1, a(1)=a(2)=0.
%F A231184 a(n) = -b(n) + b(n-1) + 4*b(n-2), n>=0, with b(n) = A231181(n).
%e A231184 rho(11)^5 = 1*1 - 3*rho(11) - 3*rho(11)^2 + 4*rho(11)^3 + 1*rho(11)^4. Approximately 26.02309649, with rho(11) approximately 1.918985947.
%t A231184 LinearRecurrence[{1,4,-3,-3,1},{-1,0,0,3,6},40] (* _Harvey P. Dale_, Apr 26 2019 *)
%Y A231184 Cf. A231181, A231182, A231183, A231185.
%K A231184 sign,easy
%O A231184 0,4
%A A231184 _Wolfdieter Lang_, Nov 07 2013