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Denominators of continued fraction convergents to sqrt(646).
2

%I #20 Sep 08 2022 08:44:55

%S 1,2,5,12,605,1222,3049,7320,369049,745418,1859885,4465188,225119285,

%T 454703758,1134526801,2723757360,137322394801,277368546962,

%U 692059488725,1661487524412,83766435709325,169194358943062,422155153595449,1013504666133960,51097388460293449

%N Denominators of continued fraction convergents to sqrt(646).

%H Vincenzo Librandi, <a href="/A042241/b042241.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 (0,0,0,610,0,0,0,-1).

%F G.f.: -(x^2 - 2*x - 1)*(x^4 + 6*x^2 + 1) / (x^8 - 610*x^4 + 1). - _Colin Barker_, Dec 05 2013

%F a(n) = 610*a(n-4) - a(n-8) for n > 7. - _Vincenzo Librandi_, Jan 18 2014

%t Denominator[Convergents[Sqrt[646], 30]] (* _Vincenzo Librandi_, Jan 18 2014 *)

%o (Magma) I:=[1,2,5,12,605,1222,3049,7320]; [n le 8 select I[n] else 610*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Jan 18 2014

%Y Cf. A042240, A040620.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 05 2013