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A041112 Numerators of continued fraction convergents to sqrt(65). 3
8, 129, 2072, 33281, 534568, 8586369, 137916472, 2215249921, 35581915208, 571525893249, 9179996207192, 147451465208321, 2368403439540328, 38041906497853569, 611038907405197432, 9814664424981012481, 157645669707101397128, 2532145379738603366529, 40671971745524755261592 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
From Philippe Deléham, Nov 21 2008: (Start)
a(n) = 16*a(n-1) + a(n-2), with n > 1, a(0) = 8, a(1) = 129.
G.f.: (8 + x)/(1 - 16*x - x^2). (End)
E.g.f.: exp(8*x)*(8*cosh(sqrt(65)*x) + sqrt(65)*sinh(sqrt(65)*x)). - Stefano Spezia, Oct 28 2022
MATHEMATICA
CoefficientList[Series[(8 + x)/(1 - 16 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)
Numerator[Convergents[Sqrt[65], 20]] (* or *) LinearRecurrence[{16, 1}, {8, 129}, 20] (* Harvey P. Dale, Nov 12 2013 *)
CROSSREFS
Sequence in context: A027951 A041115 A348546 * A348207 A356914 A364986
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 05 2013
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)