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Denominators of continued fraction convergents to sqrt(227).
2

%I #22 Sep 08 2022 08:44:54

%S 1,15,451,6780,203851,3064545,92140201,1385167560,41647167001,

%T 626092672575,18824427344251,282992502836340,8508599512434451,

%U 127911985189353105,3845868155193027601,57815934313084767120,1738323897547736041201

%N Denominators of continued fraction convergents to sqrt(227).

%H Vincenzo Librandi, <a href="/A041423/b041423.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 (0,452,0,-1).

%F G.f.: -(x^2-15*x-1) / (x^4-452*x^2+1). - _Colin Barker_, Nov 17 2013

%F a(n) = 452*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[227], 20]] (* _Harvey P. Dale_, Jul 13 2013 *)

%t CoefficientList[Series[(1 + 15 x - x^2)/(x^4 - 452 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,15,451,6780]; [n le 4 select I[n] else 452*Self(n-2)-Self(n-4): n in [1..100]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041422, A040211.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013