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%I #24 Sep 08 2022 08:44:55
%S 1,5,6,11,116,127,243,1342,59291,297797,357088,654885,6905938,7560823,
%T 14466761,79894628,3529830393,17729046593,21258876986,38987923579,
%U 411138112776,450126036355,861264149131,4756446782010,210144922557571,1055481059569865
%N Denominators of continued fraction convergents to sqrt(492).
%H Vincenzo Librandi, <a href="/A041939/b041939.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 59534, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^14 -5*x^13 +6*x^12 -11*x^11 +116*x^10 -127*x^9 +243*x^8 -1342*x^7 -243*x^6 -127*x^5 -116*x^4 -11*x^3 -6*x^2 -5*x -1) / ((x^8 -244*x^4 +1)*(x^8 +244*x^4 +1)). - _Colin Barker_, Nov 27 2013
%F a(n) = 59534*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 27 2013
%t Denominator/@Convergents[Sqrt[492], 40] (* _Harvey P. Dale_, Jun 22 2011 *)
%t CoefficientList[Series[-(x^14 - 5 x^13 + 6 x^12 - 11 x^11 + 116 x^10 - 127 x^9 + 243 x^8 - 1342 x^7 - 243 x^6 - 127 x^5 - 116 x^4 - 11 x^3 - 6 x^2 - 5 x - 1)/((x^8 - 244 x^4 + 1) (x^8 + 244 x^4 + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 27 2013 *)
%o (Magma) I:=[1,5,6,11,116,127,243,1342,59291,297797, 357088,654885,6905938,7560823,14466761,79894628]; [n le 16 select I[n] else 59534*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2013
%Y Cf. A041938, A040469.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Nov 27 2013
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