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 A041028 Numerators of continued fraction convergents to sqrt(19). 4
 4, 9, 13, 48, 61, 170, 1421, 3012, 4433, 16311, 20744, 57799, 483136, 1024071, 1507207, 5545692, 7052899, 19651490, 164264819, 348181128, 512445947, 1885518969, 2397964916, 6681448801, 55849555324 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,340,0,0,0,0,0,-1). FORMULA a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +9*x^9 -13*x^8 +48*x^7 -61*x^6 -170*x^5 -61*x^4 -48*x^3 -13*x^2 -9*x -4)/(x^12-340*x^6+1). [Colin Barker, Jul 16 2012] MATHEMATICA Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[19], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *) CoefficientList[Series[- (x^11 - 4 x^10 + 9 x^9 - 13 x^8 + 48 x^7 - 61 x^6 - 170 x^5 - 61 x^4 - 48 x^3 - 13 x^2 - 9 x - 4)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *) LinearRecurrence[{0, 0, 0, 0, 0, 340, 0, 0, 0, 0, 0, -1}, {4, 9, 13, 48, 61, 170, 1421, 3012, 4433, 16311, 20744, 57799}, 30] (* or *) Numerator[ Convergents[ Sqrt[19], 30]] (* Harvey P. Dale, Jul 04 2021 *) CROSSREFS Cf. A010124, A010475, A041029. Sequence in context: A033287 A041323 A319217 * A041211 A042323 A042083 Adjacent sequences: A041025 A041026 A041027 * A041029 A041030 A041031 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified June 3 18:44 EDT 2023. Contains 363116 sequences. (Running on oeis4.)