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Denominators of continued fraction convergents to sqrt(312).
2

%I #25 Apr 25 2023 13:38:02

%S 1,1,2,3,104,107,211,318,11023,11341,22364,33705,1168334,1202039,

%T 2370373,3572412,123832381,127404793,251237174,378641967,13125064052,

%U 13503706019,26628770071,40132476090,1391132957131,1431265433221,2822398390352,4253663823573

%N Denominators of continued fraction convergents to sqrt(312).

%H Vincenzo Librandi, <a href="/A041589/b041589.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,106,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+3*x^2+1) / (x^8-106*x^4+1). - _Colin Barker_, Nov 19 2013

%F a(n) = 106*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 20 2013

%t Denominator/@Convergents[Sqrt[312], 30] (* _Harvey P. Dale_, Jun 04 2011 *)

%t CoefficientList[Series[(1 + x - x^2) (x^4 + 3 x^2 + 1)/(x^8 - 106 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 20 2013 *)

%o (Magma) I:=[1,1,2,3,104,107,211,318]; [n le 8 select I[n] else 106*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013

%Y Cf. A041588, A040294.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Nov 19 2013