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%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