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%I #19 Sep 08 2022 08:44:55
%S 1,2,3,5,8,21,1268,2557,3825,6382,10207,26796,1617967,3262730,4880697,
%T 8143427,13024124,34191675,2064524624,4163240923,6227765547,
%U 10391006470,16618772017,43628550504,2634331802257,5312292155018,7946623957275,13258916112293
%N Denominators of continued fraction convergents to sqrt(923).
%H Vincenzo Librandi, <a href="/A042785/b042785.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1276, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^10-2*x^9+3*x^8-5*x^7+8*x^6-21*x^5-8*x^4-5*x^3-3*x^2-2*x-1) / (x^12-1276*x^6+1). - _Colin Barker_, Dec 23 2013
%F a(n) = 1276*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 23 2013
%p convert(sqrt(923), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 23 2013
%t Denominator[Convergents[Sqrt[923],30]] (* _Wesley Ivan Hurt_, Dec 23 2013 *)
%t CoefficientList[Series[-(x^10 - 2 * x^9 + 3 * x^8 - 5 * x^7 + 8 * x^6 - 21 * x^5 - 8 * x^4 - 5 * x^3 - 3 * x^2 - 2 * x - 1)/(x^12 - 1276 * x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 23 2013 *)
%t LinearRecurrence[{0,0,0,0,0,1276,0,0,0,0,0,-1},{1,2,3,5,8,21,1268,2557,3825,6382,10207,26796},30] (* _Harvey P. Dale_, Jul 04 2017 *)
%o (Magma) I:=[1,2,3,5,8,21,1268,2557,3825,6382,10207, 26796]; [n le 12 select I[n] else 1276*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013
%Y Cf. A042784, A040892.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Dec 23 2013
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