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 A228209 #37 Feb 16 2025 08:33:20
%S A228209 3,7,13,57,253,487,2163,9607,18493,82137,364813,702247,3119043,
%T A228209 13853287,26666893,118441497,526060093,1012639687,4497657843,
%U A228209 19976430247,38453641213,170792556537,758578289293,1460225726407,6485619490563,28805998562887,55450123962253
%N A228209 x-values in the solutions to x^2 - 10*y^2 = 9.
%H A228209 Vincenzo Librandi, <a href="/A228209/b228209.txt">Table of n, a(n) for n = 1..1000</a>
%H A228209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>
%H A228209 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,38,0,0,-1).
%F A228209 G.f.: -x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3) / (x^6-38*x^3+1).
%F A228209 a(n) = 38*a(n-3)-a(n-6).
%t A228209 CoefficientList[Series[-(7 x^6 + 13 x^5 + 57 x^4 - 13 x^3 - 7 x^2 - 3 x) / (x^6 - 38 x^3 + 1), {x, 1, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%t A228209 LinearRecurrence[{0,0,38,0,0,-1},{3,7,13,57,253,487},30] (* _Harvey P. Dale_, Jan 06 2014 *)
%o A228209 (PARI) Vec(-x*(7*x^5+13*x^4+57*x^3-13*x^2-7*x-3)/(x^6-38*x^3+1) + O(x^100))
%o A228209 (Magma) I:=[3,7,13,57,253,487]; [n le 6 select I[n] else 38*Self(n-3)-Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Aug 17 2013
%Y A228209 Cf. A075836.
%K A228209 nonn,easy
%O A228209 1,1
%A A228209 _Colin Barker_, Aug 16 2013
%E A228209 a(1)=3 prepended by _Max Alekseyev_, Sep 04 2013