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%I #22 Jan 01 2021 03:33:19
%S 1,102,10403,1061004,108212005,11036563506,1125621265607,
%T 114802332528408,11708712296632009,1194173851923936510,
%U 121794024183944892011,12421796292910455048612,1266901427852682470066413,129211523844680701491725514,13178308530729578869685936015
%N Chebyshev U(n,x) polynomial evaluated at x=51.
%C Used to form integer solutions of Pell equation a^2 - 26*b^2 =-1. See A097726 with A097727.
%H Indranil Ghosh, <a href="/A097725/b097725.txt">Table of n, a(n) for n = 0..496</a>
%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H R. Flórez, R. A. Higuita, and 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 (102,-1).
%F a(n) = 102*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F a(n) = S(n, 2*51)= U(n, 51), Chebyshev's polynomials of the second kind. See A049310.
%F G.f.: 1/(1-102*x+x^2).
%F a(n)= sum((-1)^k*binomial(n-k, k)*102^(n-2*k), k=0..floor(n/2)), n>=0.
%F a(n) = ((51+10*sqrt(26))^(n+1) - (51-10*sqrt(26))^(n+1))/(20*sqrt(26)).
%t ChebyshevU[Range[0,20],51] (* _Harvey P. Dale_, Oct 08 2012 *)
%t LinearRecurrence[{102, -1},{1, 102},15] (* _Ray Chandler_, Aug 11 2015 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
%E More terms from _Harvey P. Dale_, Oct 08 2012
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