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Denominators of continued fraction convergents to sqrt(333).
2

%I #19 Jul 18 2024 13:04:53

%S 1,4,145,584,21169,85260,3090529,12447376,451196065,1817231636,

%T 65871534961,265303371480,9616792908241,38732475004444,

%U 1403985893068225,5654676047277344,204972323595052609,825543970427487780,29924555258984612689,120523765006365938536

%N Denominators of continued fraction convergents to sqrt(333).

%H Vincenzo Librandi, <a href="/A041629/b041629.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, 146, 0, -1).

%F G.f.: -(x^2-4*x-1) / ((x^2-12*x-1)*(x^2+12*x-1)). - _Colin Barker_, Nov 20 2013

%F a(n) = 146*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[333], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%t LinearRecurrence[{0,146,0,-1},{1,4,145,584},20] (* _Harvey P. Dale_, Jul 18 2024 *)

%o (Magma) I:=[1,4,145,584]; [n le 4 select I[n] else 146*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041628, A040314.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 20 2013