|
%I #14 Sep 08 2022 08:44:55
%S 30,601,36090,722401,43380150,868325401,52142904210,1043726409601,
%T 62675727480270,1254558276015001,75336172288380330,
%U 1507978004043621601,90554016414905676390,1812588306302157149401,108845852394544334640450
%N Numerators of continued fraction convergents to sqrt(903).
%H Vincenzo Librandi, <a href="/A042744/b042744.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 (0,1202,0,-1).
%F G.f.: (30 +601*x +30*x^2 -x^3)/(1 -1202*x^2 +x^4). - _Vincenzo Librandi_, Dec 03 2013
%F a(n) = 1202*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 03 2013
%t Numerator[Convergents[Sqrt[903], 30]] (* or *) CoefficientList[Series[(30 + 601 x + 30 x^2 - x^3)/(1 - 1202 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)
%t LinearRecurrence[{0,1202,0,-1},{30,601,36090,722401},20] (* _Harvey P. Dale_, May 25 2022 *)
%o (Magma) I:=[30, 601, 36090, 722401]; [n le 4 select I[n] else 1202*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013
%Y Cf. A042745.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
|
