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%I #18 Sep 08 2022 08:44:55
%S 24,145,6984,42049,2025336,12194065,587340456,3536236801,170326706904,
%T 1025496478225,49394157661704,297390442448449,14324135395187256,
%U 86242202813571985,4153949870446642536
%N Numerators of continued fraction convergents to sqrt(584).
%H Vincenzo Librandi, <a href="/A042118/b042118.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, 290, 0, -1).
%F G.f.: (24+145*x+24*x^2-x^3)/(1-290*x^2+x^4). - _Vincenzo Librandi_, Nov 17 2013
%F a(n) = 290*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 17 2013
%t Numerator[Convergents[Sqrt[584], 30]] (* or *) CoefficientList[Series[(24 + 145 x + 24 x^2 - x^3)/(1 - 290 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 17 2013 *)
%o (Magma) I:=[24,145,6984,42049]; [n le 4 select I[n] else 290*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 17 2013
%Y Cf. A042119.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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