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%I #17 Sep 08 2022 08:44:54
%S 1,4,9,40,889,3596,8081,35920,798321,3229204,7256729,32256120,
%T 716891369,2899821596,6516534561,28965959840,643767651041,
%U 2604036564004,5851840779049,26011399680200,578102633743449,2338421934653996,5254946503051441,23358207946859760
%N Denominators of continued fraction convergents to sqrt(126).
%H Vincenzo Librandi, <a href="/A041229/b041229.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 (0,0,0,898,0,0,0,-1).
%F G.f.: (1 + 4*x + 9*x^2 + 40*x^3 - 9*x^4 + 4*x^5 - x^6)/(1 - 898*x^4 + x^8). - _Vincenzo Librandi_, Dec 13 2013
%F a(n) = 898*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[126], 30]] (* or *) CoefficientList[Series[(1 + 4 x + 9 x^2 + 40 x^3 - 9 x^4 + 4 x^5 - x^6)/(1 - 898 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)
%t LinearRecurrence[{0,0,0,898,0,0,0,-1},{1,4,9,40,889,3596,8081,35920},30] (* _Harvey P. Dale_, Aug 20 2017 *)
%o (Magma) I:=[1,4,9,40,889,3596,8081,35920]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041228.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 13 2013
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