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 A228210 #31 Feb 11 2024 04:18:14
%S A228210 7,8,13,17,32,43,83,112,217,293,568,767,1487,2008,3893,5257,10192,
%T A228210 13763,26683,36032,69857,94333,182888,246967,478807,646568,1253533,
%U A228210 1692737,3281792,4431643,8591843,11602192,22493737,30374933,58889368,79522607,154174367
%N A228210 x-values in the solutions to x^2 - 5y^2 = 44.
%C A228210 Also values of x (or y) in the solutions to x^2 - 3xy + y^2 + 55 = 0.
%H A228210 Vincenzo Librandi, <a href="/A228210/b228210.txt">Table of n, a(n) for n = 1..1000</a>
%H A228210 Project Euler, <a href="https://projecteuler.net/problem=140">Problem 140: Modified Fibonacci golden nuggets</a>
%H A228210 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F A228210 G.f.: -x*(x-1)*(7*x^2+15*x+7) / ((x^2-x-1)*(x^2+x-1)).
%F A228210 a(n) = 3*a(n-2)-a(n-4).
%t A228210 CoefficientList[Series[-(x - 1) (7 x^2 + 15 x + 7) / ((x^2 - x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%t A228210 LinearRecurrence[{0,3,0,-1},{7,8,13,17},40] (* _Harvey P. Dale_, Jun 01 2020 *)
%o A228210 (PARI) Vec(-x*(x-1)*(7*x^2+15*x+7)/((x^2-x-1)*(x^2+x-1)) + O(x^100))
%o A228210 (Magma) I:=[7,8,13,17]; [n le 4 select I[n] else 3*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Aug 17 2013
%Y A228210 Cf. A228208.
%K A228210 nonn,easy
%O A228210 1,1
%A A228210 _Colin Barker_, Aug 16 2013