A041385 - OEIS

%I #23 Sep 08 2022 08:44:54

%S 1,2,3,5,13,18,31,80,2271,4622,6893,11515,29923,41438,71361,184160,

%T 5227841,10639842,15867683,26507525,68882733,95390258,164272991,

%U 423936240,12034487711,24492911662,36527399373,61020311035,158568021443,219588332478

%N Denominators of continued fraction convergents to sqrt(207).

%H Vincenzo Librandi, <a href="/A041385/b041385.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 (0,0,0,0,0,0,0,2302,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +13*x^10 -18*x^9 +31*x^8 -80*x^7 -31*x^6 -18*x^5 -13*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^8 -48*x^4 +1)*(x^8 +48*x^4 +1)). - _Colin Barker_, Nov 16 2013

%F a(n) = 2302*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 16 2013

%t Denominator[Convergents[Sqrt[207],40]] (* _Harvey P. Dale_, May 03 2012 *)

%t CoefficientList[Series[-(x^14 - 2 x^13 + 3 x^12 - 5 x^11 + 13 x^10 - 18 x^9 + 31 x^8 - 80 x^7 - 31 x^6 - 18 x^5 - 13 x^4 - 5 x^3 - 3 x^2 - 2 x - 1)/((x^8 - 48 x^4 + 1) (x^8 + 48 x^4 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 16 2013 *)

%o (Magma) I:=[1,2,3,5,13,18,31,80,2271,4622,6893,11515, 29923,41438,71361,184160]; [n le 16 select I[n] else 2302*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 16 2013

%Y Cf. A041384, A040192.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 16 2013