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 A041758 #27 Jul 09 2025 01:22:51
%S A041758 19,20,779,799,31141,31940,1244861,1276801,49763299,51040100,
%T A041758 1989287099,2040327199,79521720661,81562047860,3178879539341,
%U A041758 3260441587201,127075659852979,130336101440180,5079847514579819,5210183616019999,203066824923339781
%N A041758 Numerators of continued fraction convergents to sqrt(399).
%H A041758 Vincenzo Librandi, <a href="/A041758/b041758.txt">Table of n, a(n) for n = 0..200</a>
%H A041758 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,40,0,-1).
%F A041758 G.f.: (19 + 20*x + 19*x^2 - x^3)/(1 - 40*x^2 + x^4). - _Vincenzo Librandi_, Nov 07 2013
%F A041758 a(n) = 40*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 07 2013
%t A041758 Numerator[Convergents[Sqrt[399], 30]] (* or *) CoefficientList[Series[(19 + 20 x + 19 x^2 - x^3)/(1 - 40 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 07 2013 *)
%t A041758 LinearRecurrence[{0,40,0,-1},{19,20,779,799},30] (* _Harvey P. Dale_, Sep 21 2018 *)
%o A041758 (Magma) I:=[19,20,779,799]; [n le 4 select I[n] else 40*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 07 2013
%Y A041758 Cf. A041759.
%K A041758 nonn,frac,easy
%O A041758 0,1
%A A041758 _N. J. A. Sloane_