A041667 - OEIS

%I #15 Sep 08 2022 08:44:54

%S 1,1,4,21,193,986,3151,4137,152083,156220,620743,3259935,29960158,

%T 153060725,489142333,642203058,23608452421,24250655479,96360418858,

%U 506052749769,4650835166779,23760228583664,75931520917771,99691749501435,3664834502969431

%N Denominators of continued fraction convergents to sqrt(352).

%H Vincenzo Librandi, <a href="/A041667/b041667.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 (0,0,0,0,0,0,0,155234,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^14 -x^13 +4*x^12 -21*x^11 +193*x^10 -986*x^9 +3151*x^8 -4137*x^7 -3151*x^6 -986*x^5 -193*x^4 -21*x^3 -4*x^2 -x -1) / ((x^8 -394*x^4 +1)*(x^8 +394*x^4 +1)). - _Colin Barker_, Nov 21 2013

%F a(n) = 155234*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[352], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%o (Magma) I:=[1,1,4,21,193,986,3151,4137,152083,156220, 620743,3259935,29960158,153060725,489142333,642203058]; [n le 16 select I[n] else 155234*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041666, A040333.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 21 2013