%I #18 Sep 08 2022 08:44:55
%S 24,193,9288,74497,3585144,28755649,1383856296,11099606017,
%T 534164945112,4284419166913,206186284956936,1653774698822401,
%U 79587371828432184,638352749326279873,30720519339489866088
%N Numerators of continued fraction convergents to sqrt(582).
%H Vincenzo Librandi, <a href="/A042114/b042114.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.: (24 + 193*x + 24*x^2 - x^3)/(1 - 386*x^2 + x^4). - _Vincenzo Librandi_, Nov 16 2013
%F a(n) = 386*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 17 2013
%t Numerator[Convergents[Sqrt[582], 30]] (* or *) CoefficientList[Series[(24 + 193 x + 24 x^2 - x^3)/(1 - 386 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 17 2013 *)
%o (Magma) I:=[24,193,9288,74497]; [n le 4 select I[n] else 386*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 17 2013
%Y Cf. A042115.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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