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Denominators of continued fraction convergents to sqrt(986).
2

%I #16 Sep 08 2022 08:44:55

%S 1,2,5,312,629,1570,97969,197508,492985,30762578,62018141,154798860,

%T 9659547461,19473893782,48607335025,3033128665332,6114864665689,

%U 15262857996710,952412060461709,1920086978920128,4792586018301965,299060420113641958,602913426245585881

%N Denominators of continued fraction convergents to sqrt(986).

%H Vincenzo Librandi, <a href="/A042909/b042909.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 314, 0, 0, 1).

%F G.f.: -(x^4-2*x^3+5*x^2+2*x+1) / (x^6+314*x^3-1). - _Colin Barker_, Dec 25 2013

%F a(n) = 314*a(n-3) + a(n-6) for n>5. - _Vincenzo Librandi_, Feb 01 2014

%t Denominator[Convergents[Sqrt[986], 30]] (* _Vincenzo Librandi_, Feb 01 2014 *)

%o (Magma) I:=[1,2,5,312,629,1570]; [n le 6 select I[n] else 314*Self(n-3)+Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Feb 01 2014

%Y Cf. A042908, A040954.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 25 2013