%I #20 Sep 08 2022 08:44:55
%S 30,301,18090,181201,10890150,109082701,6555852210,65667604801,
%T 3946612140270,39531789007501,2375853952590330,23798071314910801,
%U 1430260132847238390,14326399399787294701,861014224120084920450
%N Numerators of continued fraction convergents to sqrt(906).
%H Vincenzo Librandi, <a href="/A042750/b042750.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,602,0,-1).
%F G.f.: (30 +301*x +30*x^2 -x^3)/(1 -602*x^2 +x^4). - _Vincenzo Librandi_, Dec 03 2013
%F a(n) = 602*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 03 2013
%t Numerator[Convergents[Sqrt[906], 30]] (* or *) CoefficientList[Series[(30 + 301 x + 30 x^2 - x^3)/(1 - 602 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)
%t LinearRecurrence[{0,602,0,-1},{30,301,18090,181201},20] (* _Harvey P. Dale_, Jun 11 2017 *)
%o (Magma) I:=[30,301,18090,181201]; [n le 4 select I[n] else 602*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013
%Y Cf. A042751.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_