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%I #14 Feb 06 2017 08:44:35
%S 1,326,106275,34645324,11294269349,3681897162450,1200287180689351,
%T 391289939007565976,127559319829285818825,41583946974408169370974,
%U 13556239154337233929118699,4419292380366963852723324900
%N Chebyshev U(n,x) polynomial evaluated at x=163.
%C Used to form integer solutions of Pell equation a^2 - 82*b^2 =-1. See A097738 with A097739.
%H Indranil Ghosh, <a href="/A097737/b097737.txt">Table of n, a(n) for n = 0..397</a>
%H R. Flórez, R. A. Higuita, A. Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Mukherjee/mukh2.html">Alternating Sums in the Hosoya Polynomial Triangle</a>, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
%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 (326, -1).
%F a(n) = 2*163*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F a(n) = S(n, 2*163)= U(n, 163), Chebyshev's polynomials of the second kind. See A049310.
%F a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0.
%F a(n)= sum((-1)^k*binomial(n-k, k)*326^(n-2*k), k=0..floor(n/2)), n>=0.
%F G.f.: 1/(1-326*x+x^2).
%F a(n) = ((163+18*sqrt(82))^(n+1) - (163-18*sqrt(82))^(n+1))/(36*sqrt(82)), n>=0.
%t LinearRecurrence[{326, -1},{1, 326},12] (* _Ray Chandler_, Aug 11 2015 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
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