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A041429 Denominators of continued fraction convergents to sqrt(230). 2

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

%S 1,6,181,1092,32941,198738,5995081,36169224,1091071801,6582600030,

%T 198569072701,1197997036236,36138480159781,218028877994922,

%U 6577004820007441,39680057798039568,1196978738761194481,7221552490365206454,217843553449717388101

%N Denominators of continued fraction convergents to sqrt(230).

%H Vincenzo Librandi, <a href="/A041429/b041429.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, 182, 0, -1).

%F G.f.: -(x^2-6*x-1) / (x^4-182*x^2+1). - _Colin Barker_, Nov 17 2013

%F a(n) = 182*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[230], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,6,181,1092]; [n le 4 select I[n] else 182*Self(n-2)-Self(n-4): n in [1..100]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041428, A040214, A176909.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013

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