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A042098 Numerators of continued fraction convergents to sqrt(573). 2

%I

%S 23,24,359,383,17977,18360,275017,293377,13770359,14063736,210662663,

%T 224726399,10548077017,10772803416,161367324841,172140128257,

%U 8079813224663,8251953352920,123607160165543

%N Numerators of continued fraction convergents to sqrt(573).

%H Vincenzo Librandi, <a href="/A042098/b042098.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, 766, 0, 0, 0, -1).

%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 359*x^4 - 383*x^3 - 359*x^2 - 24*x - 23)/(x^8 - 766*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 766*a(n-4) - a(n-8). _Vincenzo Librandi_, Nov 16 2013

%t Numerator[Convergents[Sqrt[573], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 359 x^4 - 383 x^3 - 359 x^2 - 24 x - 23)/(x^8 - 766 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%o (MAGMA) I:=[23, 24, 359, 383, 17977, 18360, 275017, 293377]; [n le 8 select I[n] else 766*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042099.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)