%I #28 Aug 17 2024 15:59:04

%S 1,1,3,4,27,31,89,120,809,929,2667,3596,24243,27839,79921,107760,

%T 726481,834241,2394963,3229204,21770187,24999391,71768969,96768360,

%U 652379129,749147489,2150674107,2899821596

%N Denominators of continued fraction convergents to sqrt(14).

%H Vincenzo Librandi, <a href="/A041021/b041021.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 (0,0,0,30,0,0,0,-1).

%F G.f.: (1+1*x+3*x^2+4*x^3-3*x^4+x^5-x^6)/(1-30*x^4+x^8). [Colin Barker, Jan 03 2012]

%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[14],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011*)

%t Convergents[Sqrt[14],30]//Denominator (* or *) LinearRecurrence[{0,0,0,30,0,0,0,-1},{1,1,3,4,27,31,89,120},30] (* _Harvey P. Dale_, Aug 17 2024 *)

%Y Cf. A010471, A041020.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.