%I #18 Jul 09 2025 02:12:27

%S 23,24,71,95,4441,4536,13513,18049,843767,861816,2567399,3429215,

%T 160311289,163740504,487792297,651532801,30458301143,31109833944,

%U 92677969031,123787802975,5786916905881,5910704708856

%N Numerators of continued fraction convergents to sqrt(564).

%H Vincenzo Librandi, <a href="/A042080/b042080.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 (0,0,0,190,0,0,0,-1).

%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 71*x^4 - 95*x^3 - 71*x^2 -24*x - 23)/(x^8 - 190*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 190*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 16 2013

%t Numerator[Convergents[Sqrt[564], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 71 x^4 - 95 x^3 - 71 x^2 - 24 x - 23)/(x^8 - 190 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%t LinearRecurrence[{0,0,0,190,0,0,0,-1},{23,24,71,95,4441,4536,13513,18049},30] (* _Harvey P. Dale_, Apr 18 2015 *)

%o (Magma) I:=[23, 24, 71, 95, 4441, 4536, 13513, 18049]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042081.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_