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%I #21 Sep 08 2022 08:44:54
%S 1,17,579,9860,335819,5718783,194774441,3316884280,112968839961,
%T 1923787163617,65521732402939,1115793238013580,38002491824864659,
%U 647158154260712783,22041379736689099281,375350613677975400560,12783962244787852718321
%N Denominators of continued fraction convergents to sqrt(291).
%H Vincenzo Librandi, <a href="/A041547/b041547.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 (0,580,0,-1).
%F G.f.: -(x^2-17*x-1) / (x^4-580*x^2+1). - _Colin Barker_, Nov 18 2013
%F a(n) = 580*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 20 2013
%t Denominator[Convergents[Sqrt[291], 40]] (* _Harvey P. Dale_, Apr 20 2012 *)
%t CoefficientList[Series[(1 + 17 x - x^2)/(x^4 - 580 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 20 2013 *)
%o (Magma) I:=[1,17,579,9860]; [n le 4 select I[n] else 580*Self(n-2)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013
%Y Cf. A041546, A040273.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 18 2013
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