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%I #21 Mar 20 2017 16:23:13
%S 7,8,23,169,361,530,7781,8311,24403,179132,382667,561799,8247853,
%T 8809652,25867157,189879751,405626659,595506410,8742716399,9338222809,
%U 27419162017,201272356928,429963875873
%N Numerators of continued fraction convergents to sqrt(59).
%H Vincenzo Librandi, <a href="/A041102/b041102.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 (0,0,0,0,0,1060,0,0,0,0,0,-1).
%F a(n) = 1060*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-23*x^8+169*x^7-361*x^6-530*x^5-361*x^4-169*x^3-23*x^2-8*x-7)/(x^12-1060*x^6+1). [_Colin Barker_, Jul 18 2012]
%t Numerator[Convergents[Sqrt[59],40]] (* or *) LinearRecurrence[ {0,0,0,0,0,1060,0,0,0,0,0,-1},{7,8,23,169,361,530,7781,8311,24403,179132,382667,561799},40] (* _Harvey P. Dale_, Nov 25 2012 *)
%t CoefficientList[Series[- (x^11 - 7 x^10 + 8 x^9 - 23 x^8 + 169 x^7 - 361 x^6 - 530 x^5 - 361 x^4 - 169 x^3 - 23 x^2 - 8 x - 7)/(x^12 - 1060 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 25 2013 *)
%Y Cf. A010512, A041103.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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