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%I #16 Sep 08 2022 08:44:54
%S 1,3,28,31,152,183,1799,5580,224999,680577,6350192,7030769,34473268,
%T 41504037,408009601,1265532840,51029323201,154353502443,1440210845188,
%U 1594564347631,7818468235712,9413032583343,92535761485799,287020317040740,11573348443115399
%N Denominators of continued fraction convergents to sqrt(413).
%H Vincenzo Librandi, <a href="/A041785/b041785.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 226798, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^14 -3*x^13 +28*x^12 -31*x^11 +152*x^10 -183*x^9 +1799*x^8 -5580*x^7 -1799*x^6 -183*x^5 -152*x^4 -31*x^3 -28*x^2 -3*x -1) / (x^16 -226798*x^8 +1). - _Colin Barker_, Nov 24 2013
%F a(n) = 226798*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 24 2013
%t Denominator[Convergents[Sqrt[413], 30]] (* _Vincenzo Librandi_, Dec 24 2013 *)
%o (Magma) I:=[1,3,28,31,152,183,1799,5580,224999,680577, 6350192,7030769,34473268,41504037,408009601,1265532840]; [n le 16 select I[n] else 226798*Self(n-8)-Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 24 2013
%Y Cf. A041784, A040392.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 24 2013
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