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Denominators of continued fraction convergents to sqrt(87).
2

%I #20 Sep 08 2022 08:44:54

%S 1,3,55,168,3079,9405,172369,526512,9649585,29475267,540204391,

%T 1650088440,30241796311,92375477373,1693000389025,5171376644448,

%U 94777779989089,289504716611715,5305862678999959,16207092753611592,297033532244008615,907307689485637437

%N Denominators of continued fraction convergents to sqrt(87).

%H Vincenzo Librandi, <a href="/A041155/b041155.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 (0,56,0,-1).

%F G.f.: (1 +3*x -x^2)/(x^4 -56*x^2 +1), - _Vincenzo Librandi_, Dec 12 2013

%F a(n) = 56*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 12 2013

%t Denominator/@Convergents[Sqrt[87], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)

%t CoefficientList[Series[(1 + 3 x - x^2)/(x^4 - 56 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)

%o (Magma) I:=[1, 3, 55, 168]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013

%Y Cf. A041154.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.