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 A097771 Chebyshev U(n,x) polynomial evaluated at x=339=2*13^2+1. 2
 1, 678, 459683, 311664396, 211308000805, 143266512881394, 97134484425584327, 65857037174033292312, 44650974069510146603209, 30273294562090705363683390, 20525249062123428726430735211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 170*b^2 =-1. See A097772 with A097773. LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (678, -1). FORMULA a(n) = 2*339*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*339)= U(n, 339), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-2*339*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*678^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((339+26*sqrt(170))^(n+1) - (339-26*sqrt(170))^(n+1))/(52*sqrt(170)), n>=0. MATHEMATICA LinearRecurrence[{678, -1}, {1, 678}, 11] (* Ray Chandler, Aug 12 2015 *) CROSSREFS Sequence in context: A251830 A250872 A186127 * A121105 A046514 A199995 Adjacent sequences:  A097768 A097769 A097770 * A097772 A097773 A097774 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified October 19 11:26 EDT 2019. Contains 328216 sequences. (Running on oeis4.)