%I #18 Sep 08 2022 08:44:55

%S 27,82,4455,13447,730593,2205226,119812797,361643617,19648568115,

%T 59307347962,3222245358063,9726043422151,528428590154217,

%U 1595011813884802,86659066539933525,261572211433685377

%N Numerators of continued fraction convergents to sqrt(747).

%H Vincenzo Librandi, <a href="/A042438/b042438.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, 164, 0, -1).

%F G.f.: (27 + 82*x + 27*x^2 - x^3)/(1 - 164*x^2 + x^4), - _Vincenzo Librandi_, Nov 24 2013

%F a(n) = 164*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 24 2013

%t Numerator[Convergents[Sqrt[747], 30]] (* or *) CoefficientList[Series[(27 + 82 x + 27 x^2 - x^3)/(1 - 164 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 24 2013 *)

%o (Magma) I:=[27, 82, 4455, 13447]; [n le 4 select I[n] else 164*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 24 2013

%Y Cf. A042439.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_