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 A097737 Chebyshev U(n,x) polynomial evaluated at x=163. 3
 1, 326, 106275, 34645324, 11294269349, 3681897162450, 1200287180689351, 391289939007565976, 127559319829285818825, 41583946974408169370974, 13556239154337233929118699, 4419292380366963852723324900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 82*b^2 =-1. See A097738 with A097739. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..397 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 Index entries for linear recurrences with constant coefficients, signature (326, -1). FORMULA a(n) = 2*163*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*163)= U(n, 163), Chebyshev's polynomials of the second kind. See A049310. a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0. a(n)= sum((-1)^k*binomial(n-k, k)*326^(n-2*k), k=0..floor(n/2)), n>=0. G.f.: 1/(1-326*x+x^2). a(n) = ((163+18*sqrt(82))^(n+1) - (163-18*sqrt(82))^(n+1))/(36*sqrt(82)), n>=0. MATHEMATICA LinearRecurrence[{326, -1}, {1, 326}, 12] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A138817 A158271 A203723 * A236822 A126311 A097738 Adjacent sequences:  A097734 A097735 A097736 * A097738 A097739 A097740 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified August 14 17:36 EDT 2022. Contains 356122 sequences. (Running on oeis4.)