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 A098252 #38 Aug 23 2025 09:50:03
%S A098252 1,364,132131,47963189,17410505476,6319965524599,2294130074923961,
%T A098252 832762897231873244,302290637565095063611,109730668673232276217549,
%U A098252 39831930437745751171906676,14458881018233034443125905839
%N A098252 Chebyshev polynomials S(n,363) + S(n-1,363) with Diophantine property.
%C A098252 (19*a(n))^2 - 365*b(n)^2 = -4 with b(n)=A098253(n) give all positive solutions of this Pell equation.
%H A098252 Indranil Ghosh, <a href="/A098252/b098252.txt">Table of n, a(n) for n = 0..389</a>
%H A098252 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A098252 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 A098252 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A098252 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (363,-1).
%F A098252 a(n) = S(n, 363) + S(n-1, 363) = S(2*n, sqrt(365)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 363)=A098251(n).
%F A098252 a(n) = (-2/19)*i*((-1)^n)*T(2*n+1, 19*i/2) with the imaginary unit i and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
%F A098252 G.f.: (1+x)/(1-363*x+x^2).
%F A098252 a(n) = 363*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=364. - _Philippe Deléham_, Nov 18 2008
%F A098252 E.g.f.: exp(363*x/2)*(19*cosh(19*sqrt(365)*x/2) + sqrt(365)*sinh(19*sqrt(365)*x/2))/19. - _Stefano Spezia_, Aug 23 2025
%e A098252 All positive solutions of Pell equation x^2 - 365*y^2 = -4 are (19=19*1,1), (6916=19*364,362), (2510489=19*132131,131405),(911300591=19*47963189,47699653), ...
%t A098252 LinearRecurrence[{363,-1},{1,364},20] (* _Harvey P. Dale_, Feb 03 2015 *)
%Y A098252 Cf. A049310, A053120, A098251, A098253.
%K A098252 nonn,easy
%O A098252 0,2
%A A098252 _Wolfdieter Lang_, Sep 10 2004