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%I #18 Sep 08 2022 08:44:54
%S 1,2,3,8,19,46,65,176,4289,8754,13043,34840,82723,200286,283009,
%T 766304,18674305,38114914,56789219,151693352,360175923,872045198,
%U 1232221121,3336487440,81307919681,165952326802,247260246483,660472819768,1568205886019,3796884591806
%N Denominators of continued fraction convergents to sqrt(153).
%H Vincenzo Librandi, <a href="/A041281/b041281.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 (0,0,0,0,0,0,0,4354,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^2-2*x-1)*(x^4+4*x^2+1)*(x^8+22*x^4+1) / ((x^4-8*x^2-1)*(x^4+8*x^2-1)*(x^8+66*x^4+1)). - _Colin Barker_, Nov 14 2013
%F a(n) = 4354*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 14 2013
%t Denominator[Convergents[Sqrt[153], 30]] (* _Harvey P. Dale_, Mar 04 2013 *)
%t CoefficientList[Series[-(x^2 - 2 x - 1) (x^4 + 4 x^2 + 1) (x^8 + 22 x^4 + 1)/((x^4 - 8 x^2 - 1) (x^4 + 8 x^2 - 1) (x^8 + 66 x^4 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 14 2013 *)
%o (Magma) I:=[1,2,3,8,19,46,65,176,4289,8754,13043,34840, 82723,200286,283009,766304]; [n le 16 select I[n] else 4354*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013
%Y Cf. A041280, A010204.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013