A042115 - OEIS

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

%S 1,8,385,3088,148609,1191960,57362689,460093472,22141849345,

%T 177594888232,8546696484481,68551166764080,3299002701160321,

%U 26460572776046648,1273406495951399425,10213712540387242048,491531608434539017729,3942466580016699383880

%N Denominators of continued fraction convergents to sqrt(582).

%H Vincenzo Librandi, <a href="/A042115/b042115.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 386, 0, -1).

%F G.f.: -(x^2-8*x-1) / (x^4-386*x^2+1). - _Colin Barker_, Dec 02 2013

%F a(n) = 386*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Jan 15 2014

%t Denominator[Convergents[Sqrt[582], 30]] (* _Vincenzo Librandi_, Jan 15 2014 *)

%t LinearRecurrence[{0,386,0,-1},{1,8,385,3088},20] (* _Harvey P. Dale_, May 14 2021 *)

%o (Magma) I:=[1,8,385,3088]; [n le 4 select I[n] else 386*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jan 15 2014

%Y Cf. A042114, A040557.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 02 2013