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%I #16 Sep 08 2022 08:44:54
%S 21,442,18585,390727,16429119,345402226,14523322611,305335177057,
%T 12838600759005,269915951116162,11349308547637809,238605395451510151,
%U 10032775917511064151,210926899663183857322,8868962561771233071675
%N Numerators of continued fraction convergents to sqrt(443).
%H Vincenzo Librandi, <a href="/A041842/b041842.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, 884, 0, -1).
%F G.f.: -(x^3-21*x^2-442*x-21)/(x^4-884*x^2+1). - _Vincenzo Librandi_, Nov 10 2013
%F a(n) = 884*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 10 2013
%t Numerator[Convergents[Sqrt[443], 30]] (* or *) CoefficientList[Series[-(x^3 - 21 x^2 - 442 x - 21)/(x^4 - 884 x^2 + 1), {x, 0, 25}], x] (* _Vincenzo Librandi_, Nov 10 2013 *)
%o (Magma) I:=[21,442,18585,390727]; [n le 4 select I[n] else 884*Self(n-2)-Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Nov 10 2013
%Y Cf. A041843.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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