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A098251 Chebyshev polynomials S(n,363).

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%I A098251 #12 Mar 16 2017 14:07:48
%S A098251 1,363,131768,47831421,17362674055,6302602850544,2287827472073417,
%T A098251 830475069759799827,301460162495335263784,109429208510736940953765,
%U A098251 39722501229235014230952911,14419158517003799428894952928
%N A098251 Chebyshev polynomials S(n,363).
%C A098251 Used for all positive integer solutions of Pell equation x^2 - 365*y^2 = -4. See A098252 with A098253.
%H A098251 Indranil Ghosh, <a href="/A098251/b098251.txt">Table of n, a(n) for n = 0..389</a>
%H A098251 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A098251 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (363,-1).
%H A098251 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A098251 a(n)= S(n, 363)=U(n, 363/2)= S(2*n+1, sqrt(365))/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).
%F A098251 a(n)=363*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=363; a(-1):=0.
%F A098251 a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (363+19*sqrt(365))/2 and am := (363-19*sqrt(365))/2 = 1/ap.
%F A098251 G.f.: 1/(1-363*x+x^2).
%K A098251 nonn,easy
%O A098251 0,2
%A A098251 _Wolfdieter Lang_, Sep 10 2004