A041333 - OEIS

%I #17 Sep 08 2022 08:44:54

%S 1,2,5,12,317,646,1609,3864,102073,208010,518093,1244196,32867189,

%T 66978574,166824337,400627248,10583132785,21566892818,53716918421,

%U 129000729660,3407735889581,6944472508822,17296680907225,41537834323272,1097280373312297

%N Denominators of continued fraction convergents to sqrt(180).

%H Vincenzo Librandi, <a href="/A041333/b041333.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 (0,0,0,322,0,0,0,-1).

%F G.f.: -(x^2-2*x-1)*(x^4+6*x^2+1) / ((x^2-4*x-1)*(x^2+4*x-1)*(x^4+18*x^2+1)). - _Colin Barker_, Nov 15 2013

%F a(n) = 322*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 15 2013

%t Denominator[Convergents[Sqrt[180], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)

%t LinearRecurrence[{0,0,0,322,0,0,0,-1},{1,2,5,12,317,646,1609,3864},30] (* _Harvey P. Dale_, May 07 2016 *)

%o (Magma) I:=[1,2,5,12,317,646,1609,3864]; [n le 8 select I[n] else 322*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013

%Y Cf. A041332, A040166.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 15 2013