This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A230080 #16 May 19 2017 11:02:23
%S A230080 0,3,5,23,73,265,920,3245,11385,40018,140574,493911,1735243,6096533,
%T A230080 21419128,75252674,264387942,928884046,3263482673,11465714843,
%U A230080 40282921096,141527481021,497233748352,1746949771565,6137623429414
%N A230080 Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in terms of the power basis of the degree 5 number field Q(rho(11)). Coefficients of the first power.
%C A230080 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 + a(n)*rho(11) - A230081(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 A230080 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-4,-1,1).
%F A230080 G.f.: x*(3 - 4*x - x^2 + x^3)/(1 - 3*x - 3*x^2 + 4*x^3 + x^4 - x^5).
%F A230080 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)=a(-3)=a(-2)=0, a(-1)=1.
%e A230080 1/rho(11)^4 = 146*1 + 73*rho(11) - 173*rho(11)^2 - 29*rho(11)^3 + 41*rho(11)^4 (approximately 0.07374164519).
%t A230080 LinearRecurrence[{3,3,-4,-1,1},{0,3,5,23,73},30] (* _Harvey P. Dale_, May 19 2017 *)
%Y A230080 Cf. A038342, A069006, A230081.
%K A230080 nonn,easy
%O A230080 0,2
%A A230080 _Wolfdieter Lang_, Nov 04 2013