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%I #34 Jan 05 2019 15:57:58
%S 1,4,33,136,1121,4620,38081,156944,1293633,5331476,43945441,181113240,
%T 1492851361,6152518684,50713000833,209004522016,1722749176961,
%U 7100001229860,58522759015841,241191037293224
%N Denominators of continued fraction convergents to sqrt(18).
%H Vincenzo Librandi, <a href="/A041027/b041027.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,34,0,-1).
%F G.f.: (1+4*x-x^2)/(1-34*x^2+x^4). - _Colin Barker_, Jan 02 2012
%F From _Gerry Martens_, Jul 11 2015: (Start)
%F Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
%F a0(n) = ((3+2*sqrt(2))/(17+12*sqrt(2))^n+(3-2*sqrt(2))*(17+12*sqrt(2))^n)/6.
%F a1(n) = (-1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/(6*sqrt(2)). (End)
%t Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[18], n]]], {n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t a0[n_] := ((3+2*Sqrt[2])/(17+12*Sqrt[2])^n+(3-2*Sqrt[2])*(17+12*Sqrt[2])^n)/6 // Simplify
%t a1[n_] := (-1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/(6*Sqrt[2]) // Simplify
%t Flatten[MapIndexed[{a0[#], a1[#]} &,Range[20]]] (* _Gerry Martens_, Jul 11 2015 *)
%t LinearRecurrence[{0,34,0,-1},{1,4,33,136},20] (* _Harvey P. Dale_, Jan 05 2019 *)
%Y Cf. A010474, A041026.
%K nonn,cofr,frac,easy
%O 0,2
%A _N. J. A. Sloane_
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