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%I #42 Dec 26 2023 07:02:30
%S 8,129,2072,33281,534568,8586369,137916472,2215249921,35581915208,
%T 571525893249,9179996207192,147451465208321,2368403439540328,
%U 38041906497853569,611038907405197432,9814664424981012481,157645669707101397128,2532145379738603366529,40671971745524755261592
%N Numerators of continued fraction convergents to sqrt(65).
%H Vincenzo Librandi, <a href="/A041112/b041112.txt">Table of n, a(n) for n = 0..200</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,1).
%F From _Philippe Deléham_, Nov 21 2008: (Start)
%F a(n) = 16*a(n-1) + a(n-2), with n > 1, a(0) = 8, a(1) = 129.
%F G.f.: (8 + x)/(1 - 16*x - x^2). (End)
%F E.g.f.: exp(8*x)*(8*cosh(sqrt(65)*x) + sqrt(65)*sinh(sqrt(65)*x)). - _Stefano Spezia_, Oct 28 2022
%t CoefficientList[Series[(8 + x)/(1 - 16 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t Numerator[Convergents[Sqrt[65],20]] (* or *) LinearRecurrence[{16,1},{8,129},20] (* _Harvey P. Dale_, Nov 12 2013 *)
%Y Cf. A010517, A041113.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Nov 05 2013
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