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A097734
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Chebyshev U(n,x) polynomial evaluated at x=129 = 3*43.
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2
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1, 258, 66563, 17172996, 4430566405, 1143068959494, 294907360983047, 76084956064666632, 19629623757323008009, 5064366844433271399690, 1306587016240026698112011, 337094385823082454841499148
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OFFSET
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0,2
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COMMENTS
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Used to form integer solutions of Pell equation a^2 - 65*b^2 =-1. See A097735 with A097736.
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LINKS
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FORMULA
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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.
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MATHEMATICA
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LinearRecurrence[{258, -1}, {1, 258}, 12] (* Ray Chandler, Aug 11 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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