login

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

Denominators of continued fraction convergents to sqrt(689).
2

%I #19 Sep 26 2023 12:37:23

%S 1,4,209,840,43889,176396,9216481,37042320,1935417121,7778710804,

%T 406428378929,1633492226520,85348024157969,343025588858396,

%U 17922678644794561,72033740168036640,3763677167382699841,15126742409698836004,790354282471722172049

%N Denominators of continued fraction convergents to sqrt(689).

%H Vincenzo Librandi, <a href="/A042325/b042325.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 210, 0, -1).

%F G.f.: -(x^2-4*x-1) / (x^4-210*x^2+1). - _Colin Barker_, Dec 07 2013

%F a(n) = 210*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Jan 20 2014

%t Denominator[Convergents[Sqrt[689], 30]] (* _Vincenzo Librandi_, Jan 20 2014 *)

%t LinearRecurrence[{0,210,0,-1},{1,4,209,840},20] (* _Harvey P. Dale_, Sep 26 2023 *)

%o (Magma) I:=[1,4,209,840]; [n le 4 select I[n] else 210*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jan 20 2014

%Y Cf. A042324, A040662.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 07 2013