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%I #15 Jul 31 2015 13:05:23
%S 1,786,617795,485586084,381670044229,299992169177910,
%T 235793463303793031,185333362164612144456,145671786867921841749385,
%U 114497839144824403002872154,89995155896045112838415763659
%N Chebyshev U(n,x) polynomial evaluated at x=393=2*14^2+1.
%C Used to form integer solutions of Pell equation a^2 - 197*b^2 =-1. See A097775 with A097776.
%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 (786, -1).
%F a(n) = 2*393*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F a(n) = S(n, 2*393)= U(n, 393), Chebyshev's polynomials of the second kind. See A049310.
%F G.f.: 1/(1-2*393*x+x^2).
%F a(n)= sum((-1)^k*binomial(n-k, k)*786^(n-2*k), k=0..floor(n/2)), n>=0.
%F a(n) = ((393+28*sqrt(197))^(n+1) - (393-28*sqrt(197))^(n+1))/(56*sqrt(197)), n>=0.
%t LinearRecurrence[{786,-1},{1,786},30] (* or *) CoefficientList[ Series[ 1/(1-786x+x^2), {x,0,30}],x] (* _Harvey P. Dale_, Jun 15 2011 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
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