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Denominators of continued fraction convergents to sqrt(387).
2

%I #17 Sep 08 2022 08:44:54

%S 1,1,3,58,119,177,6845,7022,20889,403913,828715,1232628,47668579,

%T 48901207,145470993,2812850074,5771171141,8584021215,331963977311,

%U 340547998526,1013059974363,19588687511423,40190434997209,59779122508632,2311797090325225

%N Denominators of continued fraction convergents to sqrt(387).

%H Vincenzo Librandi, <a href="/A041735/b041735.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 6964, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^10-x^9+3*x^8-58*x^7+119*x^6-177*x^5-119*x^4-58*x^3-3*x^2-x-1) / (x^12-6964*x^6+1). - _Colin Barker_, Nov 23 2013

%F a(n) = 6964*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 23 2013

%t Denominator[Convergents[Sqrt[387], 30]] (* _Vincenzo Librandi_, Dec 23 2013 *)

%o (Magma) I:=[1,1,3,58,119,177,6845,7022,20889,403913, 828715,1232628]; [n le 12 select I[n] else 6964*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013

%Y Cf. A041734, A040367.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 23 2013