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%I #15 Sep 08 2022 08:44:55
%S 23,24,551,575,27001,27576,633673,661249,31051127,31712376,728723399,
%T 760435775,35708769049,36469204824,838031275177,874500480001,
%U 41065053355223,41939553835224,963735237730151
%N Numerators of continued fraction convergents to sqrt(574).
%H Vincenzo Librandi, <a href="/A042100/b042100.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 (0,0,0,1150,0,0,0,-1).
%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 551*x^4 - 575*x^3 - 551*x^2 - 24*x - 23)/(x^8 - 1150*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013
%F a(n) = 1150*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 16 2013
%t Numerator[Convergents[Sqrt[574], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 551 x^4 - 575 x^3 - 551 x^2 - 24 x - 23)/(x^8 - 1150 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)
%o (Magma) I:=[23,24,551,575,27001,27576,633673,661249]; [n le 8 select I[n] else 1150*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013
%Y Cf. A042101.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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