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%I #14 Feb 06 2017 08:44:45
%S 1,402,161603,64964004,26115368005,10498312974006,4220295700182407,
%T 1696548373160353608,682008225714761968009,274165610188961150786010,
%U 110213893287736667854008011,44305710936059951516160434412
%N Chebyshev U(n,x) polynomial evaluated at x=201.
%C Used to form integer solutions of Pell equation a^2 - 101*b^2 =-1. See A097741 with A097742.
%H Indranil Ghosh, <a href="/A097740/b097740.txt">Table of n, a(n) for n = 0..383</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 (402, -1).
%F a(n) = 2*201*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F a(n) = S(n, 2*201)= U(n, 201), Chebyshev's polynomials of the second kind. See A049310.
%F G.f.: 1/(1-402*x+x^2).
%F a(n)= sum((-1)^k*binomial(n-k, k)*402^(n-2*k), k=0..floor(n/2)), n>=0.
%F a(n) = ((201+20*sqrt(101))^(n+1) - (201-20*sqrt(101))^(n+1))/(40*sqrt(101)), n>=0.
%t LinearRecurrence[{402, -1},{1, 402},12] (* _Ray Chandler_, Aug 11 2015 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
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