%I #15 Jul 09 2025 00:23:09

%S 1,1,4,5,94,99,391,490,9211,9701,38314,48015,902584,950599,3754381,

%T 4704980,88444021,93149001,367891024,461040025,8666611474,9127651499,

%U 36049565971,45177217470,849239480431,894416697901,3532489574134,4426906272035,83216802470764

%N Denominators of continued fraction convergents to sqrt(96).

%H Vincenzo Librandi, <a href="/A041173/b041173.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 (0,0,0,98,0,0,0,-1).

%F G.f.: (1 +x +4*x^2 +5*x^3 -4*x^4 +x^5 -x^6)/(1 -98*x^4 +x^8). - _Vincenzo Librandi_, Dec 12 2013

%F a(n) = 98*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 12 2013

%t Denominator[Convergents[Sqrt[96],201]] (* or *) CoefficientList[Series[(1 + x + 4 x^2 + 5 x^3 - 4 x^4 + x^5 - x^6)/(1 - 98 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 12 2013 *)

%o (Magma) I:=[1, 1, 4, 5, 94, 99, 391, 490]; [n le 8 select I[n] else 98*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 12 2013

%Y Cf. A041172.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 12 2013