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%I #19 Sep 08 2022 08:44:54
%S 1,1,3,49,101,150,4901,5051,15003,245099,505201,750300,24514801,
%T 25265101,75045003,1225985149,2527015301,3753000450,122623029701,
%U 126376030151,375375090003,6132377470199,12640130030401,18772507500600,613360370049601,632132877550201
%N Denominators of continued fraction convergents to sqrt(278).
%H Vincenzo Librandi, <a href="/A041523/b041523.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 (0,0,0,0,0,5002,0,0,0,0,0,-1).
%F G.f.: -(x^10-x^9+3*x^8-49*x^7+101*x^6-150*x^5-101*x^4-49*x^3-3*x^2-x-1) / (x^12-5002*x^6+1). - _Colin Barker_, Nov 18 2013
%F a(n) = 5002*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 19 2013
%t Denominator/@Convergents[Sqrt[278], 50] (* _Harvey P. Dale_, Mar 13 2011 *)
%t CoefficientList[Series[-(x^10 - x^9 + 3 x^8 - 49 x^7 + 101 x^6 - 150 x^5 - 101 x^4 - 49 x^3 - 3 x^2 - x - 1)/(x^12 - 5002 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 19 2013 *)
%o (Magma) I:=[1,1,3,49,101,150,4901,5051,15003,245099, 505201,750300]; [n le 12 select I[n] else 5002*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2013
%Y Cf. A041522, A040261.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 18 2013
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