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%I #17 Sep 08 2022 08:44:54
%S 18,37,1350,2737,99882,202501,7389918,14982337,546754050,1108490437,
%T 40452409782,82013310001,2992931569818,6067876449637,221436483756750,
%U 448940843963137,16383306866429682,33215554576822501
%N Numerators of continued fraction convergents to sqrt(342).
%H Vincenzo Librandi, <a href="/A041646/b041646.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,74,0,-1).
%F G.f.: -(x^3-18*x^2-37*x-18)/(x^4-74*x^2+1). - _Vincenzo Librandi_, Nov 06 2013
%F a(n) = 74*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 06 2013
%t Numerator[Convergents[Sqrt[342], 30]] (* or *) CoefficientList[Series[-(x^3 - 18 x^2 - 37 x - 18)/(x^4 - 74 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 06 2013 *)
%t LinearRecurrence[{0,74,0,-1},{18,37,1350,2737},30] (* _Harvey P. Dale_, Dec 28 2017 *)
%o (Magma) I:=[18,37,1350,2737]; [n le 4 select I[n] else 74*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 06 2013
%Y Cf. A041647.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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