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 A097772 #29 Jan 23 2020 03:25:46
%S A097772 1,679,460361,312124079,211619665201,143477820882199,
%T A097772 97277750938465721,65954171658458876639,44716831106684179895521,
%U A097772 30317945536160215510286599,20555522356685519431794418601,13936613839887246014541105524879
%N A097772 Pell equation solutions (13*a(n))^2 - 170*b(n)^2 = -1 with b(n):=A097771(n), n >= 0.
%H A097772 Michael De Vlieger, <a href="/A097772/b097772.txt">Table of n, a(n) for n = 0..353</a>
%H A097772 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A097772 Giovanni Lucca, <a href="http://forumgeom.fau.edu/FG2019volume19/FG201902index.html">Integer Sequences and Circle Chains Inside a Hyperbola</a>, Forum Geometricorum (2019) Vol. 19, 11-16.
%H A097772 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A097772 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (678,-1).
%F A097772 G.f.: (1 + x)/(1 - 2*339*x + x^2).
%F A097772 a(n) = S(n, 2*339) + S(n-1, 2*339) = S(2*n, 2*sqrt(170)), with Chebyshev polynomials of the 2nd kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).
%F A097772 a(n) = ((-1)^n)*T(2*n+1, 13*i)/(13*i) with the imaginary unit i and Chebyshev polynomials of the first kind. See the T-triangle A053120.
%F A097772 a(n) = 678*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=679. - _Philippe Deléham_, Nov 18 2008
%F A097772 a(n) = (1/13)*sinh((2*n + 1)*arcsinh(13)). - _Bruno Berselli_, Apr 05 2018
%e A097772 (x,y) = (13*1=13;1), (8827=13*679;677), (5984693=13*460361;459005), ... give the positive integer solutions to x^2 - 170*y^2 =-1.
%t A097772 LinearRecurrence[{678, -1}, {1, 679}, 12] (* _Ray Chandler_, Aug 12 2015 *)
%o A097772 (PARI) x='x+O('x^99); Vec((1+x)/(1-2*339*x+x^2)) \\ _Altug Alkan_, Apr 05 2018
%Y A097772 Cf. A097771 for S(n, 2*339).
%Y A097772 Cf. similar sequences of the type (1/k)*sinh((2*n+1)*arcsinh(k)) listed in A097775.
%K A097772 nonn,easy
%O A097772 0,2
%A A097772 _Wolfdieter Lang_, Aug 31 2004