login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Denominators of continued fraction convergents to sqrt(336).
2

%I #15 Sep 08 2022 08:44:54

%S 1,3,109,330,11989,36297,1318681,3992340,145042921,439121103,

%T 15953402629,48299328990,1754729246269,5312487067797,193004263686961,

%U 584325278128680,21228714276319441,64270468107087003,2334965566131451549,7069167166501441650

%N Denominators of continued fraction convergents to sqrt(336).

%H Vincenzo Librandi, <a href="/A041635/b041635.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 (0,110,0,-1).

%F G.f.: -(x^2-3*x-1) / (x^4-110*x^2+1). - _Colin Barker_, Nov 20 2013

%F a(n) = 110*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[336], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:=[1,3,109,330]; [n le 4 select I[n] else 110*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041634, A040317.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Nov 20 2013