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 A098244 #33 Sep 08 2022 08:45:14
%S A098244 1,170,29069,4970629,849948490,145336221161,24851643870041,
%T A098244 4249485765555850,726637214266180309,124250714153751276989,
%U A098244 21246145483077202184810,3632966626892047822325521,621216047053057100415479281,106224311079445872123224631530
%N A098244 First differences of Chebyshev polynomials S(n,171)=A097844(n) with Diophantine property.
%C A098244 (13*b(n))^2 - 173*a(n)^2 = -4 with b(n)=A097845(n) give all positive solutions of this Pell equation.
%H A098244 Indranil Ghosh, <a href="/A098244/b098244.txt">Table of n, a(n) for n = 0..446</a>
%H A098244 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A098244 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 A098244 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (171,-1).
%H A098244 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A098244 a(n) = ((-1)^n)*S(2*n, 13*i) with the imaginary unit i and the S(n, x) = U(n, x/2) Chebyshev polynomials.
%F A098244 G.f.: (1-x)/(1-171*x+x^2).
%F A098244 a(n) = S(n, 171) - S(n-1, 171) = T(2*n+1, sqrt(173)/2)/(sqrt(173)/2), with S(n, x) = U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x) = 0 = U(-1, x) and T(n, x) Chebyshev's polynomials of the first kind, A053120.
%F A098244 a(n) = 171*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=170. - _Philippe Deléham_, Nov 18 2008
%e A098244 All positive solutions of Pell equation x^2 - 173*y^2 = -4 are (13=13*1,1), (2236=13*172,170), (382343=13*29411,29069), (65378417=13*5029109,4970629), ...
%t A098244 LinearRecurrence[{171,-1}, {1,170}, 20] (* _G. C. Greubel_, Aug 01 2019 *)
%o A098244 (PARI) my(x='x+O('x^20)); Vec((1-x)/(1-171*x+x^2)) \\ _G. C. Greubel_, Aug 01 2019
%o A098244 (Magma) I:=[1,170]; [n le 2 select I[n] else 171*Self(n-1) - Self(n-2): n in [1..20]]; // _G. C. Greubel_, Aug 01 2019
%o A098244 (Sage) ((1-x)/(1-171*x+x^2)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 01 2019
%o A098244 (GAP) a:=[1,170];; for n in [3..20] do a[n]:=171*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Aug 01 2019
%K A098244 nonn,easy
%O A098244 0,2
%A A098244 _Wolfdieter Lang_, Sep 10 2004