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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
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