A041823 - OEIS

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

%S 1,1,4,5,9,14,51,65,2651,2716,10799,13515,24314,37829,137801,175630,

%T 7163001,7338631,29178894,36517525,65696419,102213944,372338251,

%U 474552195,19354426051,19828978246,78841360789,98670339035,177511699824,276182038859,1006057816401

%N Denominators of continued fraction convergents to sqrt(432).

%H Vincenzo Librandi, <a href="/A041823/b041823.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 (0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+5*x^2+1)*(x^8+13*x^4+1) / ((x^8-52*x^4+1)*(x^8+52*x^4+1)). - _Colin Barker_, Nov 25 2013

%F a(n) = 2702*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 25 2013

%t Denominator[Convergents[Sqrt[432], 30]] (* _Vincenzo Librandi_, Dec 25 2013 *)

%o (Magma) I:=[1,1,4,5,9,14,51,65,2651,2716,10799,13515, 24314,37829,137801,175630]; [n le 16 select I[n] else 2702*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 25 2013

%Y Cf. A041822, A040411.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 25 2013