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A230081 Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.

%I A230081 #13 Jun 13 2015 00:54:46
%S A230081 0,4,13,50,173,613,2149,7557,26543,93264,327657,1151183,4044478,
%T A230081 14209634,49923211,175397097,616229093,2165020570,7606447024,
%U A230081 26724012524,93890464368,329868851103,1158940469863,4071748539926,14305425173111
%N A230081 Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.
%C A230081 The formula for the nonpositive powers of rho(11) := 2*cos(Pi/11) (the length ratio (smallest diagonal/side) in the regular 11-gon), when written in the power basis of the degree 5 algebraic number field Q(rho(11)) is: 1/rho(11)^n = A038342(n)*1 + A230080*rho(11) - a(n)*rho(11)^2 - A069006(n-1)*rho(11)^3 + A038342(n-1)*rho(11)^4, n >= 0, with A069006(-1) = 0 = A038342(-1).
%H A230081 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-4,-1,1).
%F A230081 G.f.: x*(4 + x - x^2) / (1 - 3*x - 3*x^2 + 4*x^3 + x^4 - x^5).
%F A230081 a(n) = 3*a(n-1) +3*a(n-2) -4*a(n-3) -a(n-4) +a(n-5) for n >= 0, with a(-5)=3, a(-4)=0, a(-3)=0, a(-2)=-1, a(-1)=0.
%e A230081 1/rho(11)^4 = 146*1 + 73*rho(11) - 173*rho(11)^2 - 29*rho(11)^3  + 41*rho(11)^4 (approximately 0.07374164519).
%Y A230081 Cf. A038342, A069006, A230080.
%K A230081 nonn,easy
%O A230081 0,2
%A A230081 _Wolfdieter Lang_, Nov 04 2013