A041687 - OEIS

%I #17 Sep 08 2022 08:44:54

%S 1,19,723,13756,523451,9959325,378977801,7210537544,274379404473,

%T 5220419222531,198650309860651,3779576306574900,143822549959706851,

%U 2736408025541005069,104127327520517899473,1981155630915381095056,75388041302304999511601

%N Denominators of continued fraction convergents to sqrt(363).

%H Vincenzo Librandi, <a href="/A041687/b041687.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 (0,724,0,-1).

%F G.f.: -(x^2-19*x-1) / (x^4-724*x^2+1). - _Colin Barker_, Nov 21 2013

%F a(n) = 724*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[363], 20]] (* _Harvey P. Dale_, Dec 10 2013 *)

%t CoefficientList[Series[(1 + 19 x - x^2)/(x^4 - 724 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:=[1,19,723,13756]; [n le 4 select I[n] else 724*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041686, A040343.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Nov 21 2013