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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
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved

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Last modified June 14 20:28 EDT 2024. Contains 373401 sequences. (Running on oeis4.)