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 A041016 Numerators of continued fraction convergents to sqrt(12). 6
 3, 7, 45, 97, 627, 1351, 8733, 18817, 121635, 262087, 1694157, 3650401, 23596563, 50843527, 328657725, 708158977, 4577611587, 9863382151, 63757904493, 137379191137, 888033051315, 1913445293767, 12368704813917 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1). FORMULA G.f.: (3+7*x+3*x^2-x^3)/(1-14*x^2+x^4). From Gerry Martens, Jul 11 2015: (Start) Interspersion of 2 sequences [a0(n),a1(n)] for n>0: a0(n) = (-((7-4*sqrt(3))^n*(3+2*sqrt(3)))+(-3+2*sqrt(3))*(7+4*sqrt(3))^n)/2. a1(n) = ((7-4*sqrt(3))^n+(7+4*sqrt(3))^n)/2. (End) MATHEMATICA Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[12], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*) Numerator[Convergents[Sqrt[12], 30]] (* Vincenzo Librandi, Oct 28 2013 *) a0[n_] := (-((7-4*Sqrt[3])^n*(3+2*Sqrt[3]))+(-3+2*Sqrt[3])*(7+4*Sqrt[3])^n)/2 //Simplify a1[n_] := ((7-4*Sqrt[3])^n+(7+4*Sqrt[3])^n)/2 // Simplify Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *) LinearRecurrence[{0, 14, 0, -1}, {3, 7, 45, 97}, 30] (* Harvey P. Dale, Jun 02 2016 *) CROSSREFS Cf. A010469, A041017. Sequence in context: A267844 A359046 A041349 * A351354 A301324 A184339 Adjacent sequences: A041013 A041014 A041015 * A041017 A041018 A041019 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified May 29 22:39 EDT 2023. Contains 363044 sequences. (Running on oeis4.)