A041389 - OEIS

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

%S 1,2,11,35,81,278,1471,3220,91631,186482,1024041,3258605,7541251,

%T 25882358,136953041,299788440,8531029361,17361847162,95340265171,

%U 303382642675,702105550521,2409699294238,12750602021711,27910903337660,794255895476191,1616422694290042

%N Denominators of continued fraction convergents to sqrt(209).

%H Vincenzo Librandi, <a href="/A041389/b041389.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 (0,0,0,0,0,0,0,93102,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -2*x^13 +11*x^12 -35*x^11 +81*x^10 -278*x^9 +1471*x^8 -3220*x^7 -1471*x^6 -278*x^5 -81*x^4 -35*x^3 -11*x^2 -2*x -1) / (x^16 -93102*x^8 +1). - _Colin Barker_, Nov 16 2013

%F a(n) = 93102*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[209], 30]] (* _Harvey P. Dale_, Nov 07 2012 *)

%t CoefficientList[Series[-(x^14 - 2 x^13 + 11 x^12 - 35 x^11 + 81 x^10 - 278 x^9 + 1471 x^8 - 3220 x^7 - 1471 x^6 - 278 x^5 - 81 x^4 - 35 x^3 - 11 x^2 - 2 x - 1)/(x^16 - 93102 x^8 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,2,11,35,81,278,1471,3220,91631,186482,1024041, 3258605,7541251,25882358,136953041,299788440]; [n le 16 select I[n] else 93102*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041388, A040194.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 16 2013