login
Denominators of continued fraction convergents to sqrt(155).
2

%I #18 Sep 08 2022 08:44:54

%S 1,2,9,20,489,998,4481,9960,243521,497002,2231529,4960060,121272969,

%T 247505998,1111296961,2470099920,60393695041,123257490002,

%U 553423655049,1230104800100,30075938857449,61381982514998,275603868917441,612589720349880,14977757157314561

%N Denominators of continued fraction convergents to sqrt(155).

%H Vincenzo Librandi, <a href="/A041285/b041285.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 (0,0,0,498,0,0,0,-1).

%F G.f.: (1 +2*x +9*x^2 +20*x^3 -9*x^4 +2*x^5 -x^6)/(1 -498*x^4 +x^8). - _Vincenzo Librandi_, Dec 14 2013

%F a(n) = 498*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 14 2013

%t Denominator/@Convergents[Sqrt[155], 40] (* _Harvey P. Dale_, Jul 18 2011 *)

%t CoefficientList[Series[(1 + 2 x + 9 x^2 + 20 x^3 - 9 x^4 + 2 x^5 - x^6)/(1 - 498 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 14 2013 *)

%o (Magma) I:=[1,2,9,20,489,998,4481,9960]; [n le 8 select I[n] else 498*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013

%Y Cf. A041284.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 14 2013