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%I #16 Sep 08 2022 08:44:55
%S 23,24,263,287,13465,13752,150985,164737,7728887,7893624,86665127,
%T 94558751,4436367673,4530926424,49745631913,54276558337,2546467315415,
%U 2600743873752,28553906052935,31154649926687
%N Numerators of continued fraction convergents to sqrt(572).
%H Vincenzo Librandi, <a href="/A042096/b042096.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 574, 0, 0, 0, -1).
%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 263*x^4 - 287*x^3 - 263*x^2 - 24*x - 23)/(x^8 - 574*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013
%F a(n) = 574*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 16 2013
%t Numerator[Convergents[Sqrt[572], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 263 x^4 - 287 x^3 - 263 x^2 - 24 x - 23)/(x^8 - 574 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)
%o (Magma) I:=[23, 24, 263, 287, 13465, 13752, 150985, 164737]; [n le 8 select I[n] else 574*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013
%Y Cf. A042097.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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