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 A041112 #42 Dec 26 2023 07:02:30
%S A041112 8,129,2072,33281,534568,8586369,137916472,2215249921,35581915208,
%T A041112 571525893249,9179996207192,147451465208321,2368403439540328,
%U A041112 38041906497853569,611038907405197432,9814664424981012481,157645669707101397128,2532145379738603366529,40671971745524755261592
%N A041112 Numerators of continued fraction convergents to sqrt(65).
%H A041112 Vincenzo Librandi, <a href="/A041112/b041112.txt">Table of n, a(n) for n = 0..200</a>
%H A041112 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041112 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,1).
%F A041112 From _Philippe Deléham_, Nov 21 2008: (Start)
%F A041112 a(n) = 16*a(n-1) + a(n-2), with n > 1, a(0) = 8, a(1) = 129.
%F A041112 G.f.: (8 + x)/(1 - 16*x - x^2). (End)
%F A041112 E.g.f.: exp(8*x)*(8*cosh(sqrt(65)*x) + sqrt(65)*sinh(sqrt(65)*x)). - _Stefano Spezia_, Oct 28 2022
%t A041112 CoefficientList[Series[(8 + x)/(1 - 16 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t A041112 Numerator[Convergents[Sqrt[65],20]] (* or *) LinearRecurrence[{16,1},{8,129},20] (* _Harvey P. Dale_, Nov 12 2013 *)
%Y A041112 Cf. A010517, A041113.
%K A041112 nonn,frac,easy
%O A041112 0,1
%A A041112 _N. J. A. Sloane_
%E A041112 More terms from _Colin Barker_, Nov 05 2013