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A098246 Chebyshev polynomials S(n,227) + S(n-1,227) with Diophantine property.

%I A098246 #27 Jan 22 2020 02:26:24
%S A098246 1,228,51755,11748157,2666779884,605347285511,137411167031113,
%T A098246 31191729568777140,7080385200945379667,1607216248885032407269,
%U A098246 364831008111701411070396,82815031625107335280572623
%N A098246 Chebyshev polynomials S(n,227) + S(n-1,227) with Diophantine property.
%C A098246 (15*a(n))^2 - 229*b(n)^2 = -4 with b(n)=A098247(n) give all positive solutions of this Pell equation.
%H A098246 Indranil Ghosh, <a href="/A098246/b098246.txt">Table of n, a(n) for n = 0..423</a>
%H A098246 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A098246 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 A098246 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A098246 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (227, -1).
%F A098246 a(n) = S(n, 227) + S(n-1, 227) = S(2*n, sqrt(229)), 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, 227)=A098245(n).
%F A098246 a(n) = (-2/15)*i*((-1)^n)*T(2*n+1, 15*i/2) with the imaginary unit i and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
%F A098246 G.f.: (1+x)/(1-227*x+x^2).
%F A098246 a(n) = 227*a(n-1) - a(n-2), n > 1; a(0)=1, a(1)=228. [_Philippe Deléham_, Nov 18 2008]
%e A098246 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 A098246 LinearRecurrence[{227,-1},{1,228},20] (* _Harvey P. Dale_, May 29 2014 *)
%K A098246 nonn,easy
%O A098246 0,2
%A A098246 _Wolfdieter Lang_, Sep 10 2004