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%I #17 Sep 08 2022 08:44:54
%S 1,1,2,3,8,19,27,46,73,1506,1579,3085,4664,12413,29490,41903,71393,
%T 113296,2337313,2450609,4787922,7238531,19264984,45768499,65033483,
%U 110801982,175835465,3627511282,3803346747,7430858029,11234204776,29899267581,71032739938
%N Denominators of continued fraction convergents to sqrt(113).
%H Vincenzo Librandi, <a href="/A041205/b041205.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 (0,0,0,0,0,0,0,0,1552,0,0,0,0,0,0,0,0,1).
%F G.f.: -(x^16 -x^15 +2*x^14 -3*x^13 +8*x^12 -19*x^11 +27*x^10 -46*x^9 +73*x^8 +46*x^7 +27*x^6 +19*x^5 +8*x^4 +3*x^3 +2*x^2 +x +1) / (x^18 +1552*x^9 -1). - _Colin Barker_, Nov 14 2013
%F a(n) = 1552*a(n-9) + a(n-18). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[113], 40]] (* _Harvey P. Dale_, Feb 05 2012 *)
%t CoefficientList[Series[-(x^16 - x^15 + 2 x^14 - 3 x^13 + 8 x^12 - 19 x^11 + 27 x^10 - 46 x^9 + 73 x^8 + 46 x^7 + 27 x^6 + 19 x^5 + 8 x^4 + 3 x^3 + 2 x^2 + x + 1)/(x^18 + 1552 x^9 - 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)
%o (Magma) I:=[1, 1, 2, 3, 8, 19, 27, 46, 73, 1506, 1579, 3085, 4664, 12413, 29490, 41903, 71393, 113296]; [n le 18 select I[n] else 1552*Self(n-9)+Self(n-18): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041204, A010178.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013