%I #21 Sep 08 2022 08:44:54
%S 1,5,6,17,23,132,5303,26647,31950,90547,122497,703032,28243777,
%T 141921917,170165694,482253305,652418999,3744348300,150426350999,
%U 755876103295,906302454294,2568481011883,3474783466177,19942398342768,801170717176897,4025795984227253
%N Denominators of continued fraction convergents to sqrt(407).
%H Vincenzo Librandi, <a href="/A041773/b041773.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 5326, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^10-5*x^9+6*x^8-17*x^7+23*x^6-132*x^5-23*x^4-17*x^3-6*x^2-5*x-1) / (x^12-5326*x^6+1). - _Colin Barker_, Nov 24 2013
%F a(n) = 5326*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 24 2013
%t Denominator[Convergents[Sqrt[407], 40]] (* _Harvey P. Dale_, Jul 13 2012 *)
%t CoefficientList[Series[-(x^10 - 5 x^9 + 6 x^8 - 17 x^7 + 23 x^6 - 132 x^5 - 23 x^4 - 17 x^3 - 6 x^2 - 5 x - 1)/(x^12 - 5326 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 24 2013 *)
%o (Magma) I:=[1,5,6,17,23,132,5303,26647,31950,90547, 122497,703032]; [n le 12 select I[n] else 5326*Self(n-6)-Self(n-12): n in [1..50]]; // _Vincenzo Librandi_, Dec 24 2013
%Y Cf. A041772, A040386.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.