A041343 - OEIS

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

%S 1,1,2,3,5,133,138,271,409,680,18089,18769,36858,55627,92485,2460237,

%T 2552722,5012959,7565681,12578640,334610321,347188961,681799282,

%U 1028988243,1710787525,45509463893,47220251418,92729715311,139949966729,232679682040

%N Denominators of continued fraction convergents to sqrt(185).

%H Vincenzo Librandi, <a href="/A041343/b041343.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 (0,0,0,0,136,0,0,0,0,1).

%F G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+136*x^5-1). - _Colin Barker_, Nov 15 2013

%F a(n) = 136*a(n-5) + a(n-10). - _Vincenzo Librandi_, Dec 16 2013

%t Denominator[Convergents[Sqrt[185], 30]] (* _Vincenzo Librandi_, Dec 16 2013 *)

%t LinearRecurrence[{0,0,0,0,136,0,0,0,0,1},{1,1,2,3,5,133,138,271,409,680},30] (* _Harvey P. Dale_, Aug 15 2016 *)

%o (Magma) I:=[1,1,2,3,5,133,138,271,409,680]; [n le 10 select I[n] else 136*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 16 2013

%Y Cf. A041342, A010227.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 15 2013