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 A041133 #23 Jul 09 2025 00:19:12
%S A041133 1,1,2,3,50,53,103,156,2599,2755,5354,8109,135098,143207,278305,
%T A041133 421512,7022497,7444009,14466506,21910515,365034746,386945261,
%U A041133 751980007,1138925268,18974784295,20113709563,39088493858,59202203421,986323748594,1045525952015
%N A041133 Denominators of continued fraction convergents to sqrt(75).
%H A041133 Vincenzo Librandi, <a href="/A041133/b041133.txt">Table of n, a(n) for n = 0..200</a>
%H A041133 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,52,0,0,0,-1).
%F A041133 G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-52*x^4+1). - _Colin Barker_, Nov 13 2013
%F A041133 a(n) = 52*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 11 2013
%t A041133 Denominator/@Convergents[Sqrt[75], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)
%t A041133 CoefficientList[Series[-(x^2 - x - 1) (x^4 + 3 x^2 + 1)/(x^8 - 52 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t A041133 LinearRecurrence[{0,0,0,52,0,0,0,-1},{1,1,2,3,50,53,103,156},40] (* _Harvey P. Dale_, Aug 03 2024 *)
%o A041133 (Magma) I:=[1, 1, 2, 3, 50, 53, 103, 156]; [n le 8 select I[n] else 52*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013
%Y A041133 Cf. A041132, A020832, A010153.
%K A041133 nonn,cofr,frac,easy
%O A041133 0,3
%A A041133 _N. J. A. Sloane_