A097734 Chebyshev U(n,x) polynomial evaluated at x=129 = 3*43.

1, 258, 66563, 17172996, 4430566405, 1143068959494, 294907360983047, 76084956064666632, 19629623757323008009, 5064366844433271399690, 1306587016240026698112011, 337094385823082454841499148

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 sequences related to Chebyshev polynomials.

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