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 A114049 #41 Feb 11 2024 05:06:14
%S A114049 1,55,6049,665335,73180801,8049222775,885341324449,97379496466615,
%T A114049 10710859270003201,1178097140203885495,129579974563157401249,
%U A114049 14252619104807110251895,1567658521554218970307201
%N A114049 x such that x^2 - 21*y^2 = 1.
%C A114049 This sequence is computed with g(1e9,21) in the PARI program.
%C A114049 A Pellian equation - _Benoit Cloitre_, Feb 03 2006
%C A114049 Numbers m such that 21*(m^2-1) is square. - _Vincenzo Librandi_, Nov 13 2010
%H A114049 Indranil Ghosh, <a href="/A114049/b114049.txt">Table of n, a(n) for n = 0..489</a> (terms 0..130 from Vincenzo Librandi)
%H A114049 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A114049 John Robertson, <a href="https://web.archive.org/web/20190501092519/http://www.jpr2718.org/">Home page</a>.
%H A114049 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (110, -1).
%F A114049 a(0)=1, a(1)=55, a(n)=110*a(n-1)-a(n-2). - _Benoit Cloitre_, Feb 03 2006
%F A114049 G.f.: (1-55*x)/(1-110*x+x^2). - _Philippe Deléham_, Nov 18 2008
%e A114049 (55^2-1)/21 = 12^2
%t A114049 Table[ Numerator@ FromContinuedFraction@ ContinuedFraction[Sqrt@21, Length@ Last@ ContinuedFraction@ Sqrt@21*n], {n, 12}] (* _Robert G. Wilson v_, Feb 28 2006 *)
%t A114049 LinearRecurrence[{110,-1},{1,55},20] (* _Harvey P. Dale_, Jan 27 2013 *)
%o A114049 (PARI) g(n,k) = for(y=0,n,x=k*y^2+1;if(issquare(x),print1(floor(sqrt(x))",")))
%o A114049 (PARI) a0=1;a1=55;for(n=2,30,a2=110*a1-a0;a0=a1;a1=a2;print1(a2,",")) \\ _Benoit Cloitre_
%K A114049 easy,nonn
%O A114049 0,2
%A A114049 _Cino Hilliard_, Feb 01 2006
%E A114049 More terms from _Benoit Cloitre_, Feb 03 2006