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A114050 x-values in the solution to x^2 - 22*y^2 = 1.

%I A114050 #41 Sep 21 2024 15:10:53
%S A114050 1,197,77617,30580901,12048797377,4747195585637,1870383011943601,
%T A114050 736926159510193157,290347036464004160257,114395995440658128948101,
%U A114050 45071731856582838801391537,17758147955498197829619317477
%N A114050 x-values in the solution to x^2 - 22*y^2 = 1.
%C A114050 A Pellian equation (Pell's equation). - _Benoit Cloitre_, Feb 03 2006
%C A114050 The corresponding values of y are in A174766. - _Vincenzo Librandi_, Dec 21 2011
%H A114050 Vincenzo Librandi, <a href="/A114050/b114050.txt">Table of n, a(n) for n = 1..200</a>
%H A114050 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A114050 John Robertson, <a href="https://web.archive.org/web/20190501092519/http://www.jpr2718.org/">Home page</a>.
%H A114050 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (394,-1).
%F A114050 a(n) = 394*a(n-1) - a(n-2); a(1)=1, a(2)=197. - _Benoit Cloitre_, Feb 03 2006
%F A114050 G.f.: x*(1-197*x)/(1 - 394*x + x^2). - _Philippe Deléham_, Nov 18 2008
%t A114050 LinearRecurrence[{394,-1},{1,197},20] (* _Harvey P. Dale_, Nov 03 2011 *)
%o A114050 (PARI) g(n,k=22) = for(y=0,n,x=k*y^2+1;if(issquare(x),print1(sqrtint(x), ", ")))
%o A114050 (PARI) a=vector(12); a[1]=1; a[2]=197; for(i=3, #a, a[i]=394*a[i-1]-a[i-2]); a \\ _Benoit Cloitre_, Feb 03 2006
%o A114050 (Magma) I:=[1,197]; [n le 2 select I[n] else 394*Self(n-1)-Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2011
%K A114050 nonn,easy
%O A114050 1,2
%A A114050 _Cino Hilliard_, Feb 01 2006
%E A114050 More terms from _Benoit Cloitre_, Feb 03 2006
%E A114050 Offset changed from 0 to 1, g.f. and formula adapted by _Vincenzo Librandi_, Dec 21 2011