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 A321173 #26 Feb 19 2019 09:19:52
%S A321173 -1,3,-9,20,-46,103,-232,521,-1171,2631,-5912,13284,-29849,67070,
%T A321173 -150705,338631,-760897,1709720,-3841706,8632235,-19396456,43583441,
%U A321173 -97931103,220049191,-494446044,1111010176,-2496417205,5609398542,-12604204113,28321389563,-63637584697
%N A321173 a(n) = -2*a(n-1) + a(n-2) + a(n-3), a(0) = -1, a(1) = 3, a(2) = -9.
%C A321173 Let {X,Y,Z} be the roots of the cubic equation t^3 + at^2 + bt + c = 0 where {a, b, c} are integers.
%C A321173 Let {u, v, w} be three numbers such that {u + v + w, u*X + v*Y + w*Z, u*X^2 + v*Y^2 + w*Z^2} are integers.
%C A321173 Then {p(n) = u*X^n + v*Y^n + w*Z^n | n = 0, 1, 2, ...} is an integer sequence with the recurrence relation: p(n) = -a*p(n-1) - b*p(n-2) - c*p(n-3).
%C A321173 Let k = Pi/7.
%C A321173 This sequence has (a, b, c) = (2, -1, -1), (u, v, w) = (2*cos(4k), 2*cos(8k), 2*cos(2k)).
%C A321173 A033304, A274975: (a, b, c) = (2, -1, -1), (u, v, w) = (2*cos(2k), 2*cos(4k), 2*cos(8k)).
%C A321173 A321174 : (a, b, c) = (2, -1, -1), (u, v, w) = (2*cos(8k), 2*cos(2k), 2*cos(4k)).
%C A321173 X = sin(2k)/sin(4k), Y = sin(4k)/sin(8k), Z = sin(8k)/sin(2k).
%H A321173 Colin Barker, <a href="/A321173/b321173.txt">Table of n, a(n) for n = 0..1000</a>
%H A321173 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,1,1).
%F A321173 G.f.: -(1 - x + 2*x^2) / (1 + 2*x - x^2 - x^3). - _Colin Barker_, Jan 11 2019
%t A321173 LinearRecurrence[{-2,1,1},{-1,3,-9},50] (* _Stefano Spezia_, Jan 11 2019 *)
%o A321173 (PARI) Vec(-(1 - x + 2*x^2) / (1 + 2*x - x^2 - x^3) + O(x^30)) \\ _Colin Barker_, Jan 11 2019
%Y A321173 Cf. A321174, A033304, A274975.
%K A321173 sign,easy
%O A321173 0,2
%A A321173 _Kai Wang_, Jan 10 2019