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 A097773 #34 Sep 08 2022 08:45:14
%S A097773 1,677,459005,311204713,210996336409,143055204880589,
%T A097773 96991217912702933,65759902689607707985,44585117032336113310897,
%U A097773 30228643588021195217080181,20494975767561338021067051821,13895563341762999157088244054457
%N A097773 Pell equation solutions (13*b(n))^2 - 170*a(n)^2 = -1 with b(n):=A097772(n), n >= 0.
%H A097773 Seiichi Manyama, <a href="/A097773/b097773.txt">Table of n, a(n) for n = 0..353</a>
%H A097773 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A097773 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 A097773 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A097773 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (678,-1).
%F A097773 a(n) = ((-1)^n)*S(2*n, 26*i) with the imaginary unit i and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
%F A097773 G.f.: (1-x)/(1-678*x+x^2).
%F A097773 a(n) = S(n, 2*339) - S(n-1, 2*339) = T(2*n+1, sqrt(170))/sqrt(170), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x) = U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.
%F A097773 a(n) = 678*a(n-1) - a(n-2), n>1; a(0)=1, a(1)=677. - _Philippe Deléham_, Nov 18 2008
%e A097773 (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 A097773 LinearRecurrence[{678, -1},{1, 677},11] (* _Ray Chandler_, Aug 12 2015 *)
%o A097773 (PARI) my(x='x+O('x^20)); Vec((1-x)/(1-678*x+x^2)) \\ _G. C. Greubel_, Aug 01 2019
%o A097773 (Magma) I:=[1,677]; [n le 2 select I[n] else 678*Self(n-1) - Self(n-2): n in [1..20]]; // _G. C. Greubel_, Aug 01 2019
%o A097773 (Sage) ((1-x)/(1-678*x+x^2)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 01 2019
%o A097773 (GAP) a:=[1,677];; for n in [3..20] do a[n]:=678*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Aug 01 2019
%Y A097773 Cf. A097771 for S(n, 678).
%Y A097773 Row 13 of array A188647.
%K A097773 nonn,easy
%O A097773 0,2
%A A097773 _Wolfdieter Lang_, Aug 31 2004