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 A097728 Chebyshev U(n,x) polynomial evaluated at x=73 = 2*6^2+1. 2
 1, 146, 21315, 3111844, 454307909, 66325842870, 9683118751111, 1413669011819336, 206385992606871945, 30130941251591484634, 4398911036739749884619, 642210880422751891669740 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Used to form integer solutions of Pell equation a^2 - 37*b^2 =-1. See A097729 with A097730. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..461 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 (146, -1) FORMULA a(n) = 2*73*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0. a(n) = S(n, 2*73)= U(n, 73), Chebyshev's polynomials of the second kind. See A049310. G.f.: 1/(1-146*x+x^2). a(n)= sum((-1)^k*binomial(n-k, k)*146^(n-2*k), k=0..floor(n/2)), n>=0. a(n) = ((73+12*sqrt(37))^(n+1) - (73-12*sqrt(37))^(n+1))/(24*sqrt(37)). MATHEMATICA LinearRecurrence[{146, -1}, {1, 146}, 12] (* Ray Chandler, Aug 11 2015 *) CROSSREFS Sequence in context: A183653 A231243 A166219 * A172877 A172911 A172933 Adjacent sequences:  A097725 A097726 A097727 * A097729 A097730 A097731 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 31 2004 STATUS approved

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Last modified July 22 19:35 EDT 2018. Contains 312918 sequences. (Running on oeis4.)