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%I #24 Sep 08 2022 08:44:54
%S 20,41,184,3721,15068,33857,1369348,2772553,12459560,251963753,
%T 1020314572,2292592897,92724030452,187740653801,843686645656,
%U 17061473566921,69089580913340,155240635393601,6278714996657380
%N Numerators of continued fraction convergents to sqrt(418).
%H Vincenzo Librandi, <a href="/A041794/b041794.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, 67714, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^11-20*x^10+41*x^9-184*x^8+3721*x^7-15068*x^6-33857*x^5-15068*x^4-3721*x^3-184*x^2-41*x-20)/(x^12-67714*x^6+1). - _Vincenzo Librandi_, Nov 09 2013
%F a(n) = 67714*a(n-6)-a(n-12). - _Vincenzo Librandi_, Nov 09 2013
%t Numerator/@Convergents[Sqrt[418], 30] (* _Harvey P. Dale_, Apr 07 2011 *)
%t CoefficientList[Series[-(x^11 - 20 x^10 + 41 x^9 - 184 x^8 + 3721 x^7 - 15068 x^6 - 33857 x^5 - 15068 x^4 - 3721 x^3 - 184 x^2 - 41 x - 20)/(x^12 - 67714 x^6 + 1), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 67714, 0, 0, 0, 0, 0, -1}, {20, 41, 184, 3721, 15068, 33857, 1369348, 2772553, 12459560, 251963753, 1020314572, 2292592897}, 30] (* _Vincenzo Librandi_, Nov 09 2013 *)
%o (Magma) I:=[20,41,184,3721,15068,33857,1369348,2772553, 12459560,251963753,1020314572,2292592897]; [n le 12 select I[n] else 67714*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 09 2013
%Y Cf. A041795.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.