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 A098247 #32 Sep 08 2022 08:45:14
%S A098247 1,226,51301,11645101,2643386626,600037119001,136205782626601,
%T A098247 30918112619119426,7018275358757483101,1593117588325329544501,
%U A098247 361630674274491049118626,82088569942721142820383601
%N A098247 First differences of Chebyshev polynomials S(n,227)=A098245(n) with Diophantine property.
%C A098247 (15*b(n))^2 - 229*a(n)^2 = -4 with b(n)=A098246(n) give all positive solutions of this Pell equation.
%H A098247 Indranil Ghosh, <a href="/A098247/b098247.txt">Table of n, a(n) for n = 0..423</a>
%H A098247 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A098247 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 A098247 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (227,-1).
%H A098247 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A098247 a(n) = S(n, 227) - S(n-1, 227) = T(2*n+1, sqrt(229)/2)/(sqrt(229)/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 second kind, A053120.
%F A098247 a(n) = ((-1)^n)*S(2*n, 15*i) with the imaginary unit i and the S(n, x) = U(n, x/2) Chebyshev polynomials.
%F A098247 G.f.: (1-x)/(1-227*x+x^2).
%F A098247 a(n) = 227*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=226. - _Philippe Deléham_, Nov 18 2008
%e A098247 All positive solutions of Pell equation x^2 - 229*y^2 = -4 are (15=15*1,1), (3420=15*228,226), (776325=15*51755,51301), (176222355=15*11748157,11645101), ...
%t A098247 LinearRecurrence[{227,-1}, {1,226}, 20] (* _G. C. Greubel_, Aug 01 2019 *)
%o A098247 (PARI) my(x='x+O('x^20)); Vec((1-x)/(1-227*x+x^2)) \\ _G. C. Greubel_, Aug 01 2019
%o A098247 (Magma) I:=[1,226]; [n le 2 select I[n] else 227*Self(n-1) - Self(n-2): n in [1..20]]; // _G. C. Greubel_, Aug 01 2019
%o A098247 (Sage) ((1-x)/(1-227*x+x^2)).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 01 2019
%o A098247 (GAP) a:=[1,226];; for n in [3..20] do a[n]:=227*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Aug 01 2019
%K A098247 nonn,easy
%O A098247 0,2
%A A098247 _Wolfdieter Lang_, Sep 10 2004