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 A274592 #44 Feb 02 2022 13:49:53
%S A274592 3,31,1011,32119,1020995,32454831,1031656755,32793751175,
%T A274592 1042430160131,33136210400191,1053316070160371,33482245865136407,
%U A274592 1064315659783638083,33831894915991351119,1075430116136187973171,34185195288781394584359,1086660638750543922795523
%N A274592 Sum of n-th powers of the roots of x^3 -31* x^2 - 25*x - 1.
%C A274592 This is one side of a two sided sequence (see A248417).
%C A274592 a(n) is x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of the polynomial
%C A274592 x^3 -31* x^2 - 25*x - 1.
%C A274592 x1 = (tan(Pi/7))^2/(tan(2*Pi/7)*tan(4*Pi/7)),
%C A274592 x2 = (tan(2*Pi/7))^2/(tan(4*Pi/7)*tan(Pi/7)),
%C A274592 x3 = (tan(4*Pi/7))^2/(tan(Pi/7)*tan(2*Pi/7)).
%H A274592 Colin Barker, <a href="/A274592/b274592.txt">Table of n, a(n) for n = 0..600</a>
%H A274592 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (31,25,1).
%F A274592 a(n) = ((tan(Pi/7))^2/(tan(2*Pi/7)*tan(4*Pi/7)))^n + ((tan(2*Pi/7))^2/(tan(4*Pi/7)*tan(Pi/7)))^n + ((tan(4*Pi/7))^2/(tan(Pi/7)*tan(2*Pi/7)))^n.
%F A274592 a(n) = 31*a(n-1) + 25*a(n-2) + a(n-3).
%F A274592 G.f.: (3-62*x-25*x^2) / (1-31*x-25*x^2-x^3). - _Colin Barker_, Jun 30 2016
%t A274592 LinearRecurrence[{31,25,1},{3,31,1011},20] (* _Harvey P. Dale_, Feb 02 2022 *)
%o A274592 (PARI) Vec((3-62*x-25*x^2)/(1-31*x-25*x^2-x^3) + O(x^20)) \\ _Colin Barker_, Jun 30 2016
%o A274592 (PARI) polsym(x^3 -31* x^2 - 25*x - 1, 30) \\ _Charles R Greathouse IV_, Jul 20 2016
%Y A274592 Cf. A248417, A274032, A274075.
%K A274592 nonn,easy
%O A274592 0,1
%A A274592 _Kai Wang_, Jun 29 2016