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 A041019 Denominators of continued fraction convergents to sqrt(13). 13
 1, 1, 2, 3, 5, 33, 38, 71, 109, 180, 1189, 1369, 2558, 3927, 6485, 42837, 49322, 92159, 141481, 233640, 1543321, 1776961, 3320282, 5097243, 8417525, 55602393, 64019918, 119622311, 183642229, 303264540, 2003229469, 2306494009, 4309723478, 6616217487, 10925940965 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,36,0,0,0,0,1). FORMULA From Johannes W. Meijer, Jun 12 2010: (Start) a(5*n) = A006190(3*n+1), a(5*n+1) = (A006190(3*n+2) - A006190(3*n+1))/2, a(5*n+2) = (A006190(3*n+2) + A006190(3*n+1))/2, a(5*n+3) = A006190(3*n+2) and a(5*n+4) = A006190(3*n+3)/2. (End) G.f.: ((1 - 2*x + 4*x^2 - 3*x^3 + x^4)*(1 + 3*x + 4*x^2 + 2*x^3 + x^4))/(1 - 36*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013 a(n) = A010122(n)*a(n-1) + a(n-2), a(0)=1, a(-1)=0. - Paul Weisenhorn, Aug 17 2018 MATHEMATICA Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *) CoefficientList[Series[((1 - 2 x + 4 x^2 - 3 x^3 + x^4) (1 + 3 x + 4 x^2 + 2 x^3 + x^4))/(1 - 36 x^5 - x^10), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2013 *) LinearRecurrence[{0, 0, 0, 0, 36, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 33, 38, 71, 109, 180}, 40] (* Harvey P. Dale, Sep 30 2016 *) PROG (MAGMA) I:=[1, 1, 2, 3, 5, 33, 38, 71, 109, 180]; [n le 10 select I[n] else 36*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013 CROSSREFS Cf. A010122 (continued fraction for sqrt(13)), A041018 (numerators). Cf. A041047, A041091, A041151, A041227, A041319, A041427 and A041551. - Johannes W. Meijer, Jun 12 2010 Sequence in context: A109845 A241722 A276043 * A041977 A261130 A271387 Adjacent sequences:  A041016 A041017 A041018 * A041020 A041021 A041022 KEYWORD nonn,cofr,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Dec 10 2013 STATUS approved

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Last modified June 20 16:26 EDT 2019. Contains 324234 sequences. (Running on oeis4.)