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%I #23 Sep 08 2022 08:44:54
%S 18,19,170,359,3042,3401,125478,128879,1156510,2441899,20691702,
%T 23133601,853501338,876634939,7866580850,16609796639,140744953962,
%U 157354750601,5805515975598,5962870726199,53508481785190,112979834296579,957347156157822
%N Numerators of continued fraction convergents to sqrt(357).
%H Vincenzo Librandi, <a href="/A041676/b041676.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 6802, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^11-18*x^10+19*x^9-170*x^8+359*x^7-3042*x^6-3401*x^5-3042*x^4-359*x^3-170*x^2-19*x-18)/(x^12-6802*x^6+1). - _Vincenzo Librandi_, Nov 06 2013
%F a(n) = 6802*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 06 2013
%t Numerator[Convergents[Sqrt[357], 30]] (* _Harvey P. Dale_, Mar 06 2012 *)
%t CoefficientList[Series[-(x^11 - 18 x^10 + 19 x^9 - 170 x^8 + 359 x^7 - 3042 x^6 - 3401 x^5 - 3042 x^4 - 359 x^3 - 170 x^2 - 19 x - 18)/(x^12 - 6802 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 06 2013 *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 6802, 0, 0, 0, 0, 0, -1}, {18, 19, 170, 359, 3042, 3401, 125478, 128879, 1156510, 2441899, 20691702, 23133601}, 30] (* _Bruno Berselli_, Nov 06 2013 *)
%o (Magma) I:=[18,19,170,359,3042,3401,125478,128879,1156510, 2441899,20691702,23133601]; [n le 12 select I[n] else 6802*Self(n-6)-Self(n-12): n in [1..25]]; // _Vincenzo Librandi_, Nov 06 2013
%Y Cf. A041677.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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