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%I #19 Sep 08 2022 08:44:54
%S 1,1,14,15,434,449,6271,6720,194431,201151,2809394,3010545,87104654,
%T 90115199,1258602241,1348717440,39022690561,40371408001,563850994574,
%U 604222402575,17482078266674,18086300669249,252603986966911,270690287636160,7831932040779391
%N Denominators of continued fraction convergents to sqrt(223).
%H Vincenzo Librandi, <a href="/A041417/b041417.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.: -(x^2-x-1)*(x^4+15*x^2+1) / (x^8-448*x^4+1). - _Colin Barker_, Nov 17 2013
%F a(n) = 448*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 17 2013
%t Denominator[Convergents[Sqrt[223], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)
%t LinearRecurrence[{0,0,0,448,0,0,0,-1},{1,1,14,15,434,449,6271,6720},30] (* _Harvey P. Dale_, Apr 19 2019 *)
%o (Magma) I:=[1,1,14,15,434,449,6271,6720]; [n le 8 select I[n] else 448*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013
%Y Cf. A041416, A040208.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 17 2013
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