login
Numerators of continued fraction convergents to sqrt(531).
2

%I #15 Sep 08 2022 08:44:55

%S 23,530,24403,561799,25867157,595506410,27419162017,631236232801,

%T 29064285870863,669109811262650,30808115603952763,709255768702176199,

%U 32656573475904057917,751810445714495508290,34615937076342697439257

%N Numerators of continued fraction convergents to sqrt(531).

%H Vincenzo Librandi, <a href="/A042014/b042014.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, 1060, 0, -1).

%F G.f.: -(x^3-23*x^2-530*x-23)/(x^4-1060*x^2+1). - _Vincenzo Librandi_, Nov 13 2013

%F a(n) = 1060*a(n-2)-a(n-4). - _Vincenzo Librandi_, Nov 13 2013

%t Numerator[Convergents[Sqrt[531], 30]] (* or *) CoefficientList[Series[-(x^3 - 23 x^2 - 530 x - 23)/(x^4 - 1060 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 13 2013 *)

%o (Magma) I:=[23, 530, 24403, 561799]; [n le 4 select I[n] else 1060*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 13 2013

%Y Cf. A042015.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.