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 A114048 #47 Jun 01 2025 01:28:44
%S A114048 1,170,57799,19651490,6681448801,2271672940850,772362118440199,
%T A114048 262600848596726810,89283516160768675201,30356132893812752841530,
%U A114048 10320995900380175197444999,3509108249996365754378458130
%N A114048 x-values in the solution to x^2 - 19*y^2 = 1.
%C A114048 This sequence is computed with g(1e9,19) in the PARI program.
%C A114048 A Pellian equation (Pell's equation). - _Benoit Cloitre_, Feb 03 2006
%C A114048 The corresponding values of y of this Pell equation are in A174765. - _Vincenzo Librandi_, Dec 21 2011
%C A114048 Also numbers k such that 19*(k-1)*(k+1) is a square. - _Bruno Berselli_, May 31 2025
%H A114048 Vincenzo Librandi, <a href="/A114048/b114048.txt">Table of n, a(n) for n = 1..200</a>
%H A114048 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A114048 John Robertson, <a href="https://web.archive.org/web/20190501092519/http://www.jpr2718.org/">Home page</a>.
%H A114048 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (340,-1).
%F A114048 a(n) = 340*a(n-1) - a(n-2) for n >= 3; a(1)=1, a(2)=170. - _Benoit Cloitre_, Feb 03 2006
%F A114048 G.f.: x*(1-170x)/(1-340x+x^2). - _Philippe Deléham_, Nov 18 2008
%F A114048 a(n) = A167774(n-1)/9. - _Hugo Pfoertner_, Feb 11 2024
%e A114048 (170^2 - 1)/19 = 39^2.
%t A114048 LinearRecurrence[{340,-1},{1,170},30] (* _Vincenzo Librandi_, Dec 21 2011 *)
%o A114048 (PARI) g(n,k) = for(y=0,n,x=k*y^2+1;if(issquare(x),print1(floor(sqrt(x))",")))
%o A114048 (PARI) a(n)=real((170+39*quadgen(4*19))^n) /* _Michael Somos_, Feb 15 2006 */
%o A114048 (PARI) a=vector(12); a[1]=1; a[2]=170; for(i=3, #a, a[i]=340*a[i-1]-a[i-2]); a \\ _Benoit Cloitre_
%o A114048 (Magma) I:=[1,170]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2011
%Y A114048 Cf. A167774, A174765.
%K A114048 nonn,easy
%O A114048 1,2
%A A114048 _Cino Hilliard_, Feb 01 2006
%E A114048 More terms from _Benoit Cloitre_, Feb 03 2006
%E A114048 Offset changed from 0 to 1 and g.f. adapted by _Vincenzo Librandi_, Dec 21 2011