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 A041160 #16 Jul 09 2025 00:21:40
%S A041160 9,19,351,721,13329,27379,506151,1039681,19220409,39480499,729869391,
%T A041160 1499219281,27715816449,56930852179,1052471155671,2161873163521,
%U A041160 39966188099049,82094249361619,1517662676608191
%N A041160 Numerators of continued fraction convergents to sqrt(90).
%H A041160 Vincenzo Librandi, <a href="/A041160/b041160.txt">Table of n, a(n) for n = 0..100</a>
%H A041160 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,38,0,-1).
%F A041160 G.f.: (1 + x)*(9 + 10*x - x^2) / (1 - 38*x^2 + x^4). [_Bruno Berselli_, Oct 30 2013]
%F A041160 a(n) = (2+(-1)^n)*((3-sqrt(10))^(n+1)+(3+sqrt(10))^(n+1))/2. [_Bruno Berselli_, Oct 30 2013]
%t A041160 Numerator[Convergents[Sqrt[90], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t A041160 Table[(2 + (-1)^n) ((3 - Sqrt[10])^(n + 1) + (3 + Sqrt[10])^(n + 1))/2, {n, 0, 30}] (* _Bruno Berselli_, Oct 30 2013 *)
%t A041160 LinearRecurrence[{0,38,0,-1},{9,19,351,721},30] (* _Harvey P. Dale_, May 12 2018 *)
%Y A041160 Cf. A010541, A041161.
%K A041160 nonn,cofr,frac,easy
%O A041160 0,1
%A A041160 _N. J. A. Sloane_