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 A097740 Chebyshev U(n,x) polynomial evaluated at x=201. 4
 1, 402, 161603, 64964004, 26115368005, 10498312974006, 4220295700182407, 1696548373160353608, 682008225714761968009, 274165610188961150786010, 110213893287736667854008011, 44305710936059951516160434412 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 101*b^2 =-1. See A097741 with A097742. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..383 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 sequences related to Chebyshev polynomials. Index entries for linear recurrences with constant coefficients, signature (402, -1). FORMULA a(n) = 2*201*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*201)= U(n, 201), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-402*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*402^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((201+20*sqrt(101))^(n+1) - (201-20*sqrt(101))^(n+1))/(40*sqrt(101)), n>=0. MATHEMATICA LinearRecurrence[{402, -1}, {1, 402}, 12] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A158312 A237177 A128767 * A325151 A213605 A083815 Adjacent sequences: A097737 A097738 A097739 * A097741 A097742 A097743 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified July 15 16:36 EDT 2024. Contains 374333 sequences. (Running on oeis4.)