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%I #23 Sep 08 2022 08:44:54
%S 20,401,16060,321601,12880100,257923601,10329824140,206854406401,
%T 8284506080180,165896976010001,6644163546480220,133049167905614401,
%U 5328610879771056260,106705266763326739601,4273539281412840640300,85577490895020139545601
%N Numerators of continued fraction convergents to sqrt(402).
%H Vincenzo Librandi, <a href="/A041762/b041762.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,802,0,-1).
%F G.f.: -(x^3-20*x^2-401*x-20) / (x^4-802*x^2+1). - _Vincenzo Librandi_, Nov 08 2013, simplified by _Colin Barker_, Dec 28 2013
%F a(n) = 802*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 08 2013, simplified by _Colin Barker_, Dec 28 2013
%t Numerator[Convergents[Sqrt[402], 30]] (* _Harvey P. Dale_, Apr 29 2013 *)
%t CoefficientList[Series[(20 + 401 x + 16060 x^2 + 321601 x^3 + 16060 x^4 - 401 x^5 + 20 x^6 - x^7)/(1 - 643202 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 08 2013 *)
%o (Magma) I:=[20,401,16060,321601,12880100,257923601, 10329824140,206854406401]; [n le 8 select I[n] else 643202*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 08 2013
%Y Cf. A041763, A040381.
%K nonn,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
%E Additional term from _Colin Barker_, Dec 28 2013
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