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Denominators of continued fraction convergents to sqrt(723).
2

%I #19 Sep 08 2022 08:44:55

%S 1,1,8,9,476,485,3871,4356,230383,234739,1873556,2108295,111504896,

%T 113613191,906797233,1020410424,53968139281,54988549705,438887987216,

%U 493876536921,26120467907108,26614344444029,212420879015311,239035223459340,12642252498900991

%N Denominators of continued fraction convergents to sqrt(723).

%H Vincenzo Librandi, <a href="/A042393/b042393.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 484, 0, 0, 0, -1).

%F G.f.: -(x^2-x-1)*(x^4+9*x^2+1) / (x^8-484*x^4+1). - _Colin Barker_, Dec 10 2013

%t Denominator[Convergents[Sqrt[723], 30]] (* _Harvey P. Dale_, May 01 2013 *)

%t CoefficientList[Series[(1 + x - x^2) (x^4 + 9 x^2 + 1)/(x^8 - 484 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 21 2014 *)

%o (Magma) I:=[1,1,8,9,476,485,3871,4356]; [n le 8 select I[n] else 484*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Jan 21 2014

%Y Cf. A042392, A040696.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 10 2013