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Denominators of continued fraction convergents to sqrt(216).
2

%I #18 Sep 08 2022 08:44:54

%S 1,1,3,10,23,33,947,980,2907,9701,22309,32010,918589,950599,2819787,

%T 9409960,21639707,31049667,891030383,922080050,2735190483,9127651499,

%U 20990493481,30118144980,864298552921,894416697901,2653131948723,8853812544070,20360757036863

%N Denominators of continued fraction convergents to sqrt(216).

%H Vincenzo Librandi, <a href="/A041403/b041403.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 (0,0,0,0,0,970,0,0,0,0,0,-1).

%F G.f.: -(x^10 -x^9 +3*x^8 -10*x^7 +23*x^6 -33*x^5 -23*x^4 -10*x^3 -3*x^2 -x -1) / ((x^4 -10*x^2 +1)*(x^8 +10*x^6 +99*x^4 +10*x^2 +1)). - _Colin Barker_, Nov 17 2013

%F a(n) = 970*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[216], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,1,3,10,23,33,947,980,2907,9701,22309, 32010]; [n le 12 select I[n] else 970*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041402, A040201.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013