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Denominators of continued fraction convergents to sqrt(33).
2

%I #24 Apr 24 2022 18:08:01

%S 1,1,3,4,43,47,137,184,1977,2161,6299,8460,90899,99359,289617,388976,

%T 4179377,4568353,13316083,17884436,192160443,210044879,612250201,

%U 822295080,8835201001,9657496081,28150193163

%N Denominators of continued fraction convergents to sqrt(33).

%H Vincenzo Librandi, <a href="/A041055/b041055.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 (0,0,0,46,0,0,0,-1).

%F a(n) = 46*a(n-4)-a(n-8). G.f.: -(x^2-x-1)*(x^4+4*x^2+1)/(x^8-46*x^4+1). [_Colin Barker_, Jul 16 2012]

%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[33], n]]], {n, 1, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011 *)

%t Denominator[Convergents[Sqrt[33], 30]] (* _Vincenzo Librandi_, Oct 23 2013 *)

%t LinearRecurrence[{0,0,0,46,0,0,0,-1},{1,1,3,4,43,47,137,184},30] (* _Harvey P. Dale_, Apr 24 2022 *)

%Y Cf. A010488, A041054.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.