%I #17 Sep 08 2022 08:44:55

%S 24,577,27720,665857,31988856,768398401,36915112104,886731088897,

%T 42600007379160,1023286908188737,49160371600438536,

%U 1180872205318713601,56731026226898691384,1362725501650887306817,65467555105469489418600

%N Numerators of continued fraction convergents to sqrt(578).

%H Vincenzo Librandi, <a href="/A042106/b042106.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 (0,1154,0,-1).

%F G.f.: -(x^3 - 24*x^2 - 577*x - 24)/(x^4 - 1154*x^2 + 1). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 1154*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 16 2013

%t Numerator[Convergents[Sqrt[578], 30]] (* or *) CoefficientList[Series[-(x^3 - 24 x^2 - 577 x - 24)/(x^4 - 1154 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%t LinearRecurrence[{0,1154,0,-1},{24,577,27720,665857},20] (* _Harvey P. Dale_, Jul 04 2015 *)

%o (Magma) I:=[24,577,27720,665857]; [n le 4 select I[n] else 1154*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042107.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.