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 A097725 Chebyshev U(n,x) polynomial evaluated at x=51. 4
 1, 102, 10403, 1061004, 108212005, 11036563506, 1125621265607, 114802332528408, 11708712296632009, 1194173851923936510, 121794024183944892011, 12421796292910455048612, 1266901427852682470066413, 129211523844680701491725514, 13178308530729578869685936015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 26*b^2 =-1. See A097726 with A097727. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..496 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5. R. Flórez, R. A. Higuita, and 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 (102,-1). FORMULA a(n) = 102*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*51)= U(n, 51), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-102*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*102^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((51+10*sqrt(26))^(n+1) - (51-10*sqrt(26))^(n+1))/(20*sqrt(26)). MATHEMATICA ChebyshevU[Range[0, 20], 51] (* Harvey P. Dale, Oct 08 2012 *) LinearRecurrence[{102, -1}, {1, 102}, 15] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A274252 A303993 A030512 * A353142 A129751 A225993 Adjacent sequences: A097722 A097723 A097724 * A097726 A097727 A097728 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 EXTENSIONS More terms from Harvey P. Dale, Oct 08 2012 STATUS approved

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Last modified July 23 12:38 EDT 2024. Contains 374549 sequences. (Running on oeis4.)