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 A041159 #25 Jul 09 2025 00:21:34
%S A041159 1,2,7,23,53,977,2007,6998,23001,53000,977001,2007002,6998007,
%T A041159 23001023,53000053,977001977,2007004007,6998013998,23001046001,
%U A041159 53000106000,977002954001,2007006014002,6998020996007,23001069002023,53000159000053,977003931002977
%N A041159 Denominators of continued fraction convergents to sqrt(89).
%H A041159 Vincenzo Librandi, <a href="/A041159/b041159.txt">Table of n, a(n) for n = 0..200</a>
%H A041159 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1000,0,0,0,0,1).
%F A041159 G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - _Colin Barker_, Nov 14 2013
%F A041159 a(n) = 1000*a(n-5) + a(n-10). - _Vincenzo Librandi_, Dec 12 2013
%t A041159 Denominator/@Convergents[Sqrt[89], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)
%t A041159 CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)
%t A041159 LinearRecurrence[{0,0,0,0,1000,0,0,0,0,1},{1,2,7,23,53,977,2007,6998,23001,53000},30] (* _Harvey P. Dale_, Feb 07 2019 *)
%o A041159 (Magma) I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013
%Y A041159 Cf. A041158, A010161, A020846, A010540.
%K A041159 nonn,frac,easy
%O A041159 0,2
%A A041159 _N. J. A. Sloane_