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%I #16 Sep 08 2022 08:44:55
%S 24,73,170,753,1676,5781,279164,843273,1965710,8706113,19377936,
%T 66839921,3227694144,9749922353,22727538850,100660077753,224047694356,
%U 772803160821,37318599413764,112728601402113
%N Numerators of continued fraction convergents to sqrt(590).
%H Vincenzo Librandi, <a href="/A042130/b042130.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 (0,0,0,0,0,11562,0,0,0,0,0,-1).
%F G.f.: -(x^11 - 24*x^10 + 73*x^9 - 170*x^8 + 753*x^7 - 1676*x^6 - 5781*x^5 - 1676*x^4 - 753*x^3 - 170*x^2 - 73*x - 24)/(x^12 - 11562*x^6 + 1). [_Vincenzo Librandi_, Nov 17 2013]
%F a(n) = 11562*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 17 2013
%t Numerator[Convergents[Sqrt[590], 30]] (* or *) CoefficientList[Series[-(x^11 - 24 x^10 + 73 x^9 - 170 x^8 + 753 x^7 - 1676 x^6 - 5781 x^5 - 1676 x^4 - 753 x^3 - 170 x^2 - 73 x - 24)/(x^12 - 11562 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 17 2013 *)
%o (Magma) I:=[24,73,170,753,1676,5781,279164,843273,1965710,8706113, 19377936,66839921]; [n le 12 select I[n] else 11562*Self(n-6)-Self(n-12): n in [1..25]]; // _Vincenzo Librandi_, Nov 17 2013
%Y Cf. A042131.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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