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%I #36 Jul 14 2015 16:52:40
%S 1,5,51,260,2651,13515,137801,702520,7163001,36517525,372338251,
%T 1898208780,19354426051,98670339035,1006057816401,5128959421040,
%U 52295652026801,266607219555045,2718367847577251,13858446457441300
%N Denominators of continued fraction convergents to sqrt(27).
%H Vincenzo Librandi, <a href="/A041043/b041043.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,52,0,-1).
%F a(n) = 52*a(n-2)-a(n-4). G.f.: -(x^2-5*x-1)/(x^4-52*x^2+1). - _Colin Barker_, Jul 15 2012
%F From _Gerry Martens_, Jul 11 2015: (Start)
%F Interspersion of 2 sequences [a0(n),a1(n)]:
%F a0(n) = ((9+5*sqrt(3))/(26+15*sqrt(3))^n+(9-5*sqrt(3))*(26+15*sqrt(3))^n)/18.
%F a1(n) = (-1/(26+15*sqrt(3))^n+(26+15*sqrt(3))^n)/(6*sqrt(3)). (End)
%t Denominator[Convergents[Sqrt[27],50]] (* _Harvey P. Dale_, Apr 22 2012 *)
%t CoefficientList[Series[- (x^2 - 5 x - 1)/(x^4 - 52 x^2 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%t a0[n_] := (9+5*Sqrt[3]+(9-5*Sqrt[3])*(26+15*Sqrt[3])^(2*n))/(18*(26+15*Sqrt[3])^n) // Simplify
%t a1[n_] := (-1+(26+15*Sqrt[3])^(2*n))/(6*Sqrt[3]*(26+15*Sqrt[3])^n) // FullSimplify
%t Flatten[MapIndexed[{a0[#],a1[#]}&,Range[10]]] (* _Gerry Martens_, Jul 10 2015 *)
%Y Cf. A010482, A041042.
%K nonn,cofr,frac,easy
%O 0,2
%A _N. J. A. Sloane_
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