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%I #19 Sep 08 2022 08:44:54
%S 1,2,5,7,54,61,176,413,6784,13981,34746,48727,375835,424562,1224959,
%T 2874480,47216639,97307758,241832155,339139913,2615811546,2954951459,
%U 8525714464,20006380387,328627800656,677261981699,1683151764054,2360413745753,18206047984325
%N Denominators of continued fraction convergents to sqrt(71).
%H Vincenzo Librandi, <a href="/A041125/b041125.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 (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^14 -2*x^13 +5*x^12 -7*x^11 +54*x^10 -61*x^9 +176*x^8 -413*x^7 -176*x^6 -61*x^5 -54*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^16 -6960*x^8 +1). - _Colin Barker_, Nov 13 2013
%F a(n) = 6960*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 11 2013
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[71],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 26 2011 *)
%t Denominator[Convergents[Sqrt[71], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1},{1,2,5,7,54,61,176,413,6784,13981,34746,48727,375835,424562,1224959,2874480},30] (* _Harvey P. Dale_, Apr 09 2022 *)
%o (Magma) I:=[1, 2, 5, 7, 54, 61, 176, 413, 6784, 13981, 34746, 48727, 375835, 424562, 1224959, 2874480]; [n le 16 select I[n] else 6960*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2013
%Y Cf. A041124, A010150, A020828, A010523.
%K nonn,cofr,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 13 2013
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