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%I #22 Sep 08 2022 08:44:54
%S 1,2,5,17,22,61,83,310,703,1716,41887,85490,212867,724091,936958,
%T 2598007,3534965,13202902,29940769,73084440,1783967329,3641019098,
%U 9066005525,30839035673,39905041198,110649118069,150554159267,562311595870,1275177351007
%N Denominators of continued fraction convergents to sqrt(154).
%H Vincenzo Librandi, <a href="/A041283/b041283.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 (0,0,0,0,0,0,0,0,0,42590,0,0,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^18 -2*x^17 +5*x^16 -17*x^15 +22*x^14 -61*x^13 +83*x^12 -310*x^11 +703*x^10 -1716*x^9 -703*x^8 -310*x^7 -83*x^6 -61*x^5 -22*x^4 -17*x^3 -5*x^2 -2*x -1) / (x^20 -42590*x^10 +1). - _Colin Barker_, Nov 14 2013
%F a(n) = 42590*af(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 14 2013
%t Denominator/@Convergents[Sqrt[154],30] (* _Harvey P. Dale_, Jul 13 2011 *)
%t CoefficientList[Series[-(x^18 - 2 x^17 + 5 x^16 - 17 x^15 + 22 x^14 - 61 x^13 + 83 x^12 - 310 x^11 + 703 x^10 - 1716 x^9 - 703 x^8 - 310 x^7 - 83 x^6 - 61 x^5 - 22 x^4 - 17 x^3 - 5 x^2 - 2 x - 1)/(x^20 - 42590 x^10 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 14 2013 *)
%o (Magma) I:=[1,2,5,17,22,61,83,310,703,1716,41887,85490, 212867,724091,936958,2598007,3534965,13202902,29940769, 73084440]; [n le 20 select I[n] else 42590*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013
%Y Cf. A041282, A010205.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013
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