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 A041144 Numerators of continued fraction convergents to sqrt(82). 2
 9, 163, 2943, 53137, 959409, 17322499, 312764391, 5647081537, 101960232057, 1840931258563, 33238722886191, 600137943210001, 10835721700666209, 195643128555201763, 3532412035694297943, 63779059771052564737, 1151555487914640463209, 20791777842234580902499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (18,1). FORMULA From Philippe Deléham, Nov 21 2008: (Start) a(n) = 18*a(n-1) + a(n-2), n > 1; a(0)=9, a(1)=163. G.f.: (9+x)/(1-18*x-x^2). (End) a(n) = (9/2)*((9-sqrt(82))^n + (9+sqrt(82))^n) + (1/2)*sqrt(82)*((9+sqrt(82))^n - (9-sqrt(82))^n), with n >= 0. - Paolo P. Lava, Nov 28 2008 MATHEMATICA CoefficientList[Series[(9 + x)/(1 - 18 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *) CROSSREFS Cf. A010533, A041145. Sequence in context: A077280 A297436 A041147 * A212334 A086759 A053130 Adjacent sequences:  A041141 A041142 A041143 * A041145 A041146 A041147 KEYWORD nonn,cofr,frac,easy AUTHOR EXTENSIONS More terms from Colin Barker, Nov 05 2013 STATUS approved

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Last modified October 20 23:28 EDT 2020. Contains 337910 sequences. (Running on oeis4.)