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 A097734 Chebyshev U(n,x) polynomial evaluated at x=129 = 3*43. 2
 1, 258, 66563, 17172996, 4430566405, 1143068959494, 294907360983047, 76084956064666632, 19629623757323008009, 5064366844433271399690, 1306587016240026698112011, 337094385823082454841499148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 65*b^2 =-1. See A097735 with A097736. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..413 R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014). Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (258, -1). FORMULA a(n) = 2*129*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*129)= U(n, 129), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-258*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*258^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0. MATHEMATICA LinearRecurrence[{258, -1}, {1, 258}, 12] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A219991 A168125 A271038 * A121915 A239655 A246243 Adjacent sequences:  A097731 A097732 A097733 * A097735 A097736 A097737 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified August 14 17:54 EDT 2022. Contains 356122 sequences. (Running on oeis4.)