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%I #14 Jan 10 2016 08:52:19
%S 14,15,209,224,6481,6705,93646,100351,2903474,3003825,41953199,
%T 44957024,1300749871,1345706895,18794939506,20140646401,582733038734,
%U 602873685135,8420090945489,9022964630624
%N Numerators of continued fraction convergents to sqrt(223).
%H Vincenzo Librandi, <a href="/A041416/b041416.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,448,0,0,0,-1).
%F G.f.: (14 +15*x +209*x^2 +224*x^3 +209*x^4 -15*x^5 +14*x^6 -x^7) / (1 -448*x^4 +x^8). - _Vincenzo Librandi_, Nov 02 2013
%F a(0)=14, a(1)=15, a(2)=209, a(3)=224, a(4)=6481, a(5)=6705, a(6)=93646, a(7)=100351, a(n)=448*a(n-4)-a(n-8). - _Harvey P. Dale_, Jan 10 2016
%t Numerator[Convergents[Sqrt[223], 30]] (* or *) CoefficientList[Series[(14 + 15 x + 209 x^2 + 224 x^3 + 209 x^4 - 15 x^5 + 14 x^6 - x^7)/(1 - 448 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 02 2013 *)
%t LinearRecurrence[{0,0,0,448,0,0,0,-1},{14,15,209,224,6481,6705,93646,100351},30] (* _Harvey P. Dale_, Jan 10 2016 *)
%Y Cf. A041417.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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