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Denominators of continued fraction convergents to sqrt(79).
2

%I #22 Sep 08 2022 08:44:54

%S 1,1,8,9,152,161,1279,1440,24319,25759,204632,230391,3890888,4121279,

%T 32739841,36861120,622517761,659378881,5238169928,5897548809,

%U 99598950872,105496499681,838074448639,943570948320,15935209621759,16878780570079

%N Denominators of continued fraction convergents to sqrt(79).

%H Vincenzo Librandi, <a href="/A041141/b041141.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 (0,0,0,160,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-160*x^4+1). - _Colin Barker_, Nov 13 2013

%F a(n) = 160*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 11 2013

%t Denominator/@Convergents[Sqrt[79], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)

%t CoefficientList[Series[-(x^2 - x - 1) (x^4 + 9 x^2 + 1)/(x^8 - 160 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 11 2013 *)

%t LinearRecurrence[{0,0,0,160,0,0,0,-1},{1,1,8,9,152,161,1279,1440},40] (* _Harvey P. Dale_, Aug 09 2021 *)

%o (Magma) I:=[1,1,8,9,152,161,1279,1440]; [n le 8 select I[n] else 160*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013

%Y Cf. A041140, A010157, A020836, A010531.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.