A041161 - OEIS

%I #14 Sep 08 2022 08:44:54

%S 1,2,37,76,1405,2886,53353,109592,2026009,4161610,76934989,158031588,

%T 2921503573,6001038734,110940200785,227881440304,4212806126257,

%U 8653493692818,159975692596981,328604878886780

%N Denominators of continued fraction convergents to sqrt(90).

%H Vincenzo Librandi, <a href="/A041161/b041161.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 (0,38,0,-1).

%F G.f.: (1 +2*x -x^2)/(x^4 -38*x^2 +1). - _Vincenzo Librandi_, Dec 12 2013

%F a(n) = 38*a(n-2) - a(n-4), - _Vincenzo Librandi_, Dec 12 2013

%t Denominator[Convergents[Sqrt[90],30]] (* _Harvey P. Dale_, May 20 2013 *)

%t CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 38 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)

%o (Magma) I:=[1, 2, 37, 76]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 12 2013

%Y Cf. A041160.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.