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 A321461 #66 Feb 19 2019 09:20:10
%S A321461 -1,-2,-4,-1,-9,3,-22,19,-60,76,-177,269,-547,908,-1733,3002,-5560,
%T A321461 9831,-17949,32051,-58118,104271,-188456,338880,-611521,1100825,
%U A321461 -1984987,3575116,-6444265,11609510,-20922924
%N A321461 a(n) = -a(n-1) + 2*a(n-2) + a(n-3), a(0) = -1, a(1) = -2, a(2) = -4.
%C A321461 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 A321461 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 A321461 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 A321461 Let k = Pi/7.
%C A321461 This sequence has (a, b, c) = (1, -2, -1), (u, v, w) = (2*cos(4k), 2*cos(8k), 2*cos(2k)).
%C A321461 A094648: (a, b, c) = (1, -2, -1), (u, v, w) = (2*cos(8k), 2*cos(2k), 2*cos(4k)).
%C A321461 A321175: (a, b, c) = (1, -2, -1), (u, v, w) = (2*cos(2k), 2*cos(4k), 2*cos(8k)).
%C A321461 X = sin(2k)/sin(8k), Y = sin(4k)/sin(2k), Z = sin(8k)/sin(4k).
%H A321461 Colin Barker, <a href="/A321461/b321461.txt">Table of n, a(n) for n = 0..1000</a>
%H A321461 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,1).
%F A321461 G.f.: -(1 + 3*x + 4*x^2) / (1 + x - 2*x^2 - x^3). - _Colin Barker_, Feb 19 2019
%o A321461 (PARI) Vec(-(1 + 3*x + 4*x^2) / (1 + x - 2*x^2 - x^3) + O(x^40)) \\ _Colin Barker_, Feb 19 2019
%Y A321461 Cf. A321175, A094648.
%K A321461 sign,easy
%O A321461 0,2
%A A321461 _Kai Wang_, Jan 10 2019
%E A321461 Title corrected by _Colin Barker_, Jan 12 2019