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A042746 Numerators of continued fraction convergents to sqrt(904). 2

%I

%S 30,451,27090,406801,24435150,366934051,22040478210,330974107201,

%T 19880486910270,298538277761251,17932177152585330,269281195566541201,

%U 16174803911145057390,242891339862742402051,14589655195675689180450,219087719274998080108801

%N Numerators of continued fraction convergents to sqrt(904).

%H Vincenzo Librandi, <a href="/A042746/b042746.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 902, 0, -1).

%F G.f.: -(x^3-30*x^2-451*x-30) / ((x^2-30*x-1)*(x^2+30*x-1)). - _Colin Barker_, Nov 09 2013

%F a(n) = 902*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 03 2013

%t Numerator[Convergents[Sqrt[904], 30]] (* _Vincenzo Librandi_, Sep 25 2013 *)

%t CoefficientList[Series[(30 + 451 x + 30 x^2 - x^3)/(1 - 902 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)

%o (MAGMA) I:=[30, 451, 27090, 406801]; [n le 4 select I[n] else 902*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013

%Y Cf. A042747.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Nov 09 2013

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Last modified August 11 09:56 EDT 2020. Contains 336423 sequences. (Running on oeis4.)