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%I #18 Sep 08 2022 08:44:55
%S 1,1,5,6,281,287,1429,1716,80365,82081,408689,490770,22984109,
%T 23474879,116883625,140358504,6573374809,6713733313,33428308061,
%U 40142041374,1879962211265,1920104252639,9560379221821,11480483474460,537662619046981,549143102521441
%N Denominators of continued fraction convergents to sqrt(568).
%H Vincenzo Librandi, <a href="/A042089/b042089.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,286,0,0,0,-1).
%F G.f.: (1 + x - x^2)*(1 + 6*x^2 + x^4)/(1 - 286*x^4 + x^8). - _Colin Barker_, Dec 01 2013
%F a(n) = 286*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Jan 14 2014
%t Denominator[Convergents[Sqrt[568], 30]] (* _Vincenzo Librandi_, Jan 14 2014 *)
%t LinearRecurrence[{0,0,0,286,0,0,0,-1},{1,1,5,6,281,287,1429,1716},40] (* _Harvey P. Dale_, Sep 15 2019 *)
%o (Magma) I:=[1,1,5,6,281,287,1429,1716]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Jan 14 2014
%Y Cf. A042088, A040544.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Dec 01 2013
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