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 A041062 Numerators of continued fraction convergents to sqrt(38). 2
 6, 37, 450, 2737, 33294, 202501, 2463306, 14982337, 182251350, 1108490437, 13484136594, 82013310001, 997643856606, 6067876449637, 73812161252250, 448940843963137, 5461102288809894, 33215554576822501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 Index entries for linear recurrences with constant coefficients, signature (0,74,0,-1). FORMULA G.f.: -(x^3-6*x^2-37*x-6) / (x^4-74*x^2+1). - Colin Barker, Nov 04 2013 From Gerry Martens, Jul 11 2015: (start) Interspersion of 2 sequences [a0(n),a1(n)] for n>0: a0(n) = (-3+sqrt(19/2))*(37+6*sqrt(38))^n-(6+sqrt(38))/(2*(37+6*sqrt(38))^n). a1(n) = (1/(37+6*sqrt(38))^n+(37+6*sqrt(38))^n)/2. (End) MATHEMATICA Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[38], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*) Numerator[Convergents[Sqrt[38], 30]] (* Vincenzo Librandi, Oct 29 2013 *) a0[n_] := (-3+Sqrt[19/2])*(37+6*Sqrt[38])^n-(6+Sqrt[38])/(2*(37+6*Sqrt[38])^n) // Simplify a1[n_] := (1/(37+6*Sqrt[38])^n+(37+6*Sqrt[38])^n)/2 // FullSimplify Flatten[MapIndexed[{a0[#], a1[#]}&, Range[20]]] (* Gerry Martens, Jul 11 2015 *) LinearRecurrence[{0, 74, 0, -1}, {6, 37, 450, 2737}, 20] (* Harvey P. Dale, Oct 17 2020 *) CROSSREFS Cf. A041063, A010492. Sequence in context: A340029 A185036 A185236 * A240324 A283636 A211988 Adjacent sequences: A041059 A041060 A041061 * A041063 A041064 A041065 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified June 1 02:11 EDT 2023. Contains 363068 sequences. (Running on oeis4.)