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

%S 27,487,26325,474337,25640523,462003751,24973843077,449991179137,

%T 24324497516475,438290946475687,23692035607203573,426894931876140001,

%U 23076018356918763627,415795225356413885287,22476018187603268569125

%N Numerators of continued fraction convergents to sqrt(732).

%H Vincenzo Librandi, <a href="/A042408/b042408.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, 974, 0, -1).

%F G.f.: (27 +487*x +27*x^2 -x^3)/(1 -974*x^2 +x^4). - _Vincenzo Librandi_, Nov 23 2013

%F a(n) = 974*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 23 2013

%t Numerator[Convergents[Sqrt[732], 30]] (* or *) CoefficientList[Series[(27 + 487 x + 27 x^2 - x^3)/(1 - 974 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 23 2013 *)

%t LinearRecurrence[{0,974,0,-1},{27,487,26325,474337},20] (* _Harvey P. Dale_, May 07 2015 *)

%o (Magma) I:=[27, 487, 26325, 474337]; [n le 4 select I[n] else 974*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 23 2013

%Y Cf. A042409.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.