A041037 - OEIS

%I #30 Jun 22 2021 12:56:49

%S 1,1,4,5,44,49,191,240,2111,2351,9164,11515,101284,112799,439681,

%T 552480,4859521,5412001,21095524,26507525,233155724,259663249,

%U 1012145471,1271808720,11186615231,12458423951

%N Denominators of continued fraction convergents to sqrt(23).

%H Vincenzo Librandi, <a href="/A041037/b041037.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 (0,0,0,48,0,0,0,-1).

%F G.f.: (1+x+4*x^2+5*x^3-4*x^4+x^5-x^6)/(1-48*x^4+x^8). [_Colin Barker_, Jan 03 2012]

%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[23],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)

%t Denominator[Convergents[Sqrt[23],30]] (* or *) LinearRecurrence[ {0,0,0,48,0,0,0,-1},{1,1,4,5,44,49,191,240},30] (* _Harvey P. Dale_, Jun 22 2021 *)

%Y Cf. A010479, A041036.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.