A042108 - OEIS

%I #20 Jul 09 2025 02:15:11

%S 24,385,18504,296449,14248056,228265345,10970984616,175764019201,

%T 8447643906264,135338066519425,6504674836838664,104210135455938049,

%U 5008591176721865016,80241668963005778305,3856608701400999223656

%N Numerators of continued fraction convergents to sqrt(579).

%H Vincenzo Librandi, <a href="/A042108/b042108.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, 770, 0, -1).

%F G.f.: (24 + 385*x + 24*x^2 - x^3)/(1 - 770*x^2 + x^4). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 770*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 16 2013

%t Numerator[Convergents[Sqrt[579], 30]] (* or *) CoefficientList[Series[(24 + 385 x + 24 x^2 - x^3)/(1 - 770 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%t LinearRecurrence[{0,770,0,-1},{24,385,18504,296449},20] (* _Harvey P. Dale_, Nov 06 2021 *)

%o (Magma) I:=[24, 385, 18504, 296449]; [n le 4 select I[n] else 770*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042109.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_