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%I #25 Nov 13 2023 14:26:29
%S 19,20,779,799,31141,31940,1244861,1276801,49763299,51040100,
%T 1989287099,2040327199,79521720661,81562047860,3178879539341,
%U 3260441587201,127075659852979,130336101440180,5079847514579819,5210183616019999,203066824923339781
%N Numerators of continued fraction convergents to sqrt(399).
%H Vincenzo Librandi, <a href="/A041758/b041758.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 (0,40,0,-1).
%F G.f.: (19 + 20*x + 19*x^2 - x^3)/(1 - 40*x^2 + x^4). - _Vincenzo Librandi_, Nov 07 2013
%F a(n) = 40*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 07 2013
%t Numerator[Convergents[Sqrt[399], 30]] (* or *) CoefficientList[Series[(19 + 20 x + 19 x^2 - x^3)/(1 - 40 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 07 2013 *)
%t LinearRecurrence[{0,40,0,-1},{19,20,779,799},30] (* _Harvey P. Dale_, Sep 21 2018 *)
%o (Magma) I:=[19,20,779,799]; [n le 4 select I[n] else 40*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 07 2013
%Y Cf. A041759.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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