login
Denominators of continued fraction convergents to sqrt(123).
2

%I #16 Sep 08 2022 08:44:54

%S 1,11,243,2684,59291,654885,14466761,159789256,3529830393,38987923579,

%T 861264149131,9512893564020,210144922557571,2321107041697301,

%U 51274499839898193,566340605280577424,12510767816012601521,138184786581419194155,3052576072607234872931

%N Denominators of continued fraction convergents to sqrt(123).

%H Vincenzo Librandi, <a href="/A041223/b041223.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 (0,244,0,-1).

%F G.f.: (1 + 11*x - x^2)/(1 - 244*x^2 + x^4). - _Vincenzo Librandi_, Dec 13 2013

%F a(n) = 244*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 13 2013

%t Denominator[Convergents[Sqrt[123], 30]] (* or *) CoefficientList[Series[(1 + 11 x - x^2)/(1 - 244 x^2 + x^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)

%t LinearRecurrence[{0,244,0,-1},{1,11,243,2684},20] (* _Harvey P. Dale_, Jul 27 2015 *)

%o (Magma) I:=[1,11,243,2684]; [n le 4 select I[n] else 244*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013

%Y Cf. A041222.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 13 2012