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%I #11 Jul 31 2015 13:11:52
%S 1,627,393128,246490629,154549231255,96902121506256,60757475635191257,
%T 38094840321143411883,23885404123881284059384,
%U 14976110290833243961821885,9389997266948320082778262511
%N Chebyshev polynomials S(n,627).
%C Used for all positive integer solutions of Pell equation x^2 - 629*y^2 = -4. See A098261 with A098262.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (627, -1).
%F a(n)= S(n, 627)=U(n, 627/2)= S(2*n+1, sqrt(629))/sqrt(629) with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x).
%F a(n)=627*a(n-1)-a(n-2), n >= 1; a(0)=1, a(1)=627; a(-1):=0.
%F a(n)=(ap^(n+1) - am^(n+1))/(ap-am) with ap := (627+25*sqrt(629))/2 and am := (627-25*sqrt(629))/2 = 1/ap.
%F G.f.: 1/(1-627*x+x^2).
%t LinearRecurrence[{627,-1},{1,627},20] (* _Harvey P. Dale_, Aug 28 2012 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 10 2004
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