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%I #14 Sep 08 2022 08:44:55
%S 23,24,167,191,8953,9144,63817,72961,3420023,3492984,24377927,
%T 27870911,1306439833,1334310744,9312304297,10646615041,499056596183,
%U 509703211224,3557275863527,4066979074751
%N Numerators of continued fraction convergents to sqrt(570).
%H Vincenzo Librandi, <a href="/A042092/b042092.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 (0,0,0,382,0,0,0,-1).
%F G.f.: -(x^7 - 23*x^6 + 24*x^5 - 167*x^4 - 191*x^3 - 167*x^2 - 24*x - 23)/(x^8 - 382*x^4 + 1). - _Vincenzo Librandi_, Nov 16 2013
%F a(n) = 382*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 16 2013
%t Numerator[Convergents[Sqrt[570], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 167 x^4 - 191 x^3 - 167 x^2 - 24 x - 23)/(x^8 - 382 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)
%o (Magma) I:=[23, 24, 167, 191, 8953, 9144, 63817, 72961]; [n le 8 select I[n] else 382*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013
%Y Cf. A042093.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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