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%I #16 Sep 08 2022 08:44:54
%S 1,1,3,4,7,11,18,29,76,105,2176,2281,6738,9019,15757,24776,40533,
%T 65309,171151,236460,4900351,5136811,15173973,20310784,35484757,
%U 55795541,91280298,147075839,385431976,532507815,11035588276,11568096091,34171780458,45739876549
%N Denominators of continued fraction convergents to sqrt(115).
%H Vincenzo Librandi, <a href="/A041209/b041209.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 (0,0,0,0,0,0,0,0,0,2252,0,0,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^2-x-1)*(x^16+4*x^14+11*x^12+29*x^10+105*x^8+29*x^6+11*x^4+4*x^2+1) / (x^20-2252*x^10+1). - _Colin Barker_, Nov 14 2013
%F a(n) = 2252*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[115],30]] (* _Harvey P. Dale_, Oct 22 2012 *)
%t CoefficientList[Series[-(x^2 - x - 1) (x^16 + 4 x^14 + 11 x^12 + 29 x^10 + 105 x^8 + 29 x^6 + 11 x^4 + 4 x^2 + 1)/(x^20 - 2252 x^10 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)
%o (Magma) I:=[1, 1, 3, 4, 7, 11, 18, 29, 76, 105, 2176, 2281, 6738, 9019, 15757, 24776, 40533, 65309, 171151, 236460]; [n le 20 select I[n] else 2252*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041208, A010180.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013
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