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%I #22 Sep 08 2022 08:44:54
%S 1,9,163,1476,26731,242055,4383721,39695544,718903513,6509827161,
%T 117895792411,1067571958860,19334191051891,175075291425879,
%U 3170689436717713,28711280221885296,519973733430653041,4708474881097762665,85272521593190381011,772161169219811191764
%N Denominators of continued fraction convergents to sqrt(83).
%H Vincenzo Librandi, <a href="/A041147/b041147.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 (0,164,0,-1).
%F G.f.: -(x^2-9*x-1) / (x^4-164*x^2+1). - _Colin Barker_, Nov 13 2013
%F a(n) = 164*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 11 2013
%t Denominator/@Convergents[Sqrt[83], 50] (* _Vladimir Joseph Stephan Orlovsky_, Jul 05 2011 *)
%t CoefficientList[Series[(1 + 9 x - x^2)/(x^4 - 164 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t LinearRecurrence[{0,164,0,-1},{1,9,163,1476},30] (* _Harvey P. Dale_, Nov 09 2017 *)
%o (Magma) I:=[1, 9, 163, 1476]; [n le 4 select I[n] else 164*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 11 2013
%Y Cf. A041146, A040073, A020840, A010534.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
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