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 A274664 #28 Jul 11 2016 15:33:04 %S A274664 3,-11,129,-1460,165655,-187926,2131986,-24186985,274396853, %T A274664 -3112981337,35316195134,-400655674969,4545364223858,-51566312967180, %U A274664 585010243859443,-6636832570098735,75293632933556677,-854192282305658944,9690652804526376357,-109938656346079219026,1247233638742671255770 %N A274664 Sum of n-th powers of the roots of x^3 + 11*x^2 - 4*x - 1. %C A274664 This is the other half for A274663. %C A274664 a(n) is x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of the polynomial x^3 + 11*x^2 - 3*x - 1. %C A274664 x1 = (cos(2*Pi/7)*cos(4*Pi/7))/(cos(Pi/7))^2, %C A274664 x2 = -(cos(4*Pi/7)*cos(Pi/7))/(cos(2*Pi/7))^2, %C A274664 x3 = -(cos(Pi/7) *cos(2*Pi/7))(cos(4*Pi/7))^2. %H A274664 Colin Barker, <a href="/A274664/b274664.txt">Table of n, a(n) for n = 0..900</a> %H A274664 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-11,4,1). %F A274664 a(0) = 3, a(1) = -11, a(2) = 129; thereafter a(n) = -11*a(n-1) + 4*a(n-2) + a(n-3). %F A274664 a(n) = ((cos(2*Pi/7)*cos(4*Pi/7))/(cos(Pi/7))^2)^n +(-(cos(4*Pi/7)*cos(Pi/7))/(cos(2*Pi/7))^2)^n +(-(cos(Pi/7)*cos(2*Pi/7))/(cos(4*Pi/7))^2)^n. %F A274664 G.f.: (3+22*x-4*x^2+149090*x^4+1639990*x^5-596360*x^6-149090*x^7) / (1+11*x-4*x^2-x^3). - _Colin Barker_, Jul 03 2016 %o A274664 (PARI) Vec((3+22*x-4*x^2+149090*x^4+1639990*x^5-596360*x^6-149090*x^7) / (1+11*x-4*x^2-x^3) + O(x^20)) \\ _Colin Barker_, Jul 03 2016 %o A274664 (PARI) first(n)=my(x='x); polsym(x^3+11*x^2-4*x-1,n) \\ _Charles R Greathouse IV_, Jul 10 2016 %Y A274664 Cf. A274663. %K A274664 sign,easy %O A274664 0,1 %A A274664 _Kai Wang_, Jul 01 2016