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%I #14 Feb 06 2017 09:44:39
%S 1,146,21315,3111844,454307909,66325842870,9683118751111,
%T 1413669011819336,206385992606871945,30130941251591484634,
%U 4398911036739749884619,642210880422751891669740
%N Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1.
%C Used to form integer solutions of Pell equation a^2 - 37*b^2 =-1. See A097729 with A097730.
%H Indranil Ghosh, <a href="/A097728/b097728.txt">Table of n, a(n) for n = 0..461</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 (146, -1)
%F a(n) = 2*73*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F a(n) = S(n, 2*73)= U(n, 73), Chebyshev's polynomials of the second kind. See A049310.
%F G.f.: 1/(1-146*x+x^2).
%F a(n)= sum((-1)^k*binomial(n-k, k)*146^(n-2*k), k=0..floor(n/2)), n>=0.
%F a(n) = ((73+12*sqrt(37))^(n+1) - (73-12*sqrt(37))^(n+1))/(24*sqrt(37)).
%t LinearRecurrence[{146, -1},{1, 146},12] (* _Ray Chandler_, Aug 11 2015 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
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