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 A041010 Numerators of continued fraction convergents to sqrt(8). 2
 2, 3, 14, 17, 82, 99, 478, 577, 2786, 3363, 16238, 19601, 94642, 114243, 551614, 665857, 3215042, 3880899, 18738638, 22619537, 109216786, 131836323, 636562078, 768398401, 3710155682, 4478554083, 21624372014, 26102926097 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi,  Table of n, a(n) for n = 0..199 [1 removed by Georg Fischer, Jul 01 2019] Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1). FORMULA a(n) = 6*a(n-2) - a(n-4). a(2n) = a(2n-1) + a(2n-2), a(2n+1) = 4*a(2n) + a(2n-1). a(2n) = A001333(2n), a(2n+1) = 2*A001333(2n+1). G.f.: (2+3*x+2*x^2-x^3)/(1-6*x^2+x^4). a(n) = A001333(n+1)*A000034(n+1). - R. J. Mathar, Jul 08 2009 From Gerry Martens, Jul 11 2015: (Start) Interspersion of 2 sequences [a0(n),a1(n)] for n>0: a0(n) = -((3-2*sqrt(2))^n*(1+sqrt(2)))+(-1+sqrt(2))*(3+2*sqrt(2))^n. a1(n) = ((3-2*sqrt(2))^n+(3+2*sqrt(2))^n)/2. (End) MATHEMATICA Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[8], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*) CoefficientList[Series[(2 + 3*x + 2*x^2 - x^3)/(1 - 6*x^2 + x^4), {x, 0, 30}], x]  (* Vincenzo Librandi_, Oct 28 2013 *) a0[n_] := -((3-2*Sqrt[2])^n*(1+Sqrt[2]))+(-1+Sqrt[2])*(3+2*Sqrt[2])^n // Simplify a1[n_] := ((3-2*Sqrt[2])^n+(3+2*Sqrt[2])^n)/2 // Simplify Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *) CROSSREFS Cf. A010466, A041011. Sequence in context: A042367 A100341 A041869 * A041733 A212112 A107083 Adjacent sequences:  A041007 A041008 A041009 * A041011 A041012 A041013 KEYWORD nonn,cofr,frac,easy AUTHOR EXTENSIONS Entry improved by Michael Somos First term 1 removed in b-file, formulas and programs by Georg Fischer, Jul 01 2019 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)