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%I #14 Sep 08 2022 08:44:55
%S 23,24,119,143,6697,6840,34057,40897,1915319,1956216,9740183,11696399,
%T 547774537,559470936,2785658281,3345129217,156661602263,160006731480,
%U 796688528183,956695259663,44804670472681
%N Numerators of continued fraction convergents to sqrt(568).
%H Vincenzo Librandi, <a href="/A042088/b042088.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 (0,0,0,286,0,0,0,-1).
%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 119*x^4 - 143*x^3 - 119*x^2 - 24*x - 23)/(x^8 - 286*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013
%F a(n) = 286*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 16 2013
%t Numerator[Convergents[Sqrt[568], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 119 x^4 - 143 x^3 - 119 x^2 - 24 x - 23)/(x^8 - 286 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)
%o (Magma) I:=[23, 24, 119, 143, 6697, 6840, 34057, 40897]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013
%Y Cf. A042089.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.