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A041581 Denominators of continued fraction convergents to sqrt(308). 2

%I

%S 1,1,2,9,11,20,691,711,1402,6319,7721,14040,485081,499121,984202,

%T 4435929,5420131,9856060,340526171,350382231,690908402,3114015839,

%U 3804924241,6918940080,239048886961,245967827041,485016714002,2186034683049,2671051397051

%N Denominators of continued fraction convergents to sqrt(308).

%H Vincenzo Librandi, <a href="/A041581/b041581.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 (0,0,0,0,0,702,0,0,0,0,0,-1).

%F G.f.: -(x^4 -x^3 +2*x^2 +x +1)*(x^6 -10*x^3 -1) / ((x^4 -9*x^2 +1)*(x^8 +9*x^6 +80*x^4 +9*x^2 +1)). - _Colin Barker_, Nov 19 2013

%F a(n) = 702*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 20 2013

%t Denominator[Convergents[Sqrt[308], 30]] (* _Harvey P. Dale_, Nov 25 2011 *)

%t CoefficientList[Series[-(x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 10 x^3 - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 20 2013 *)

%o (MAGMA) I:=[1,1,2,9,11,20,691,711,1402,6319,7721,14040]; [n le 12 select I[n] else 702*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013

%Y Cf. A041580, A040290.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 19 2013

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Last modified April 19 08:44 EDT 2019. Contains 322241 sequences. (Running on oeis4.)