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 A042208 #19 Jul 09 2025 02:24:51
%S A042208 25,251,12575,126001,6312625,63252251,3168925175,31752504001,
%T A042208 1590794125225,15939693756251,798575481937775,8001694513134001,
%U A042208 400883301138637825,4016834705899512251,201242618596114250375
%N A042208 Numerators of continued fraction convergents to sqrt(630).
%H A042208 Vincenzo Librandi, <a href="/A042208/b042208.txt">Table of n, a(n) for n = 0..200</a>
%H A042208 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,502,0,-1).
%F A042208 G.f.: (25 +251*x +25*x^2 -x^3)/(x^4 -502*x^2 +1). - _Vincenzo Librandi_, Nov 19 2013
%F A042208 a(n) = 502*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 19 2013
%t A042208 Numerator[Convergents[Sqrt[630], 30]] (* or *) CoefficientList[Series[(25 + 251 x + 25 x^2 - x^3)/(x^4 - 502 x^2 + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)
%t A042208 LinearRecurrence[{0,502,0,-1},{25,251,12575,126001},20] (* _Harvey P. Dale_, Apr 01 2018 *)
%o A042208 (Magma) I:=[25,251,12575,126001]; [n le 4 select I[n] else 502*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013
%Y A042208 Cf. A042209.
%K A042208 nonn,cofr,frac,easy
%O A042208 0,1
%A A042208 _N. J. A. Sloane_