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%I #9 Jan 16 2024 09:32:40
%S 2,3,8,27,98,363,1352,5043,18818,70227,262088,978123,3650402,13623483,
%T 50843528,189750627,708158978,2642885283,9863382152,36810643323,
%U 137379191138,512706121227,1913445293768,7141075053843,26650854921602
%N a(n) = ((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,1).
%F a(n) = ((2+sqrt(3))^n+(2-sqrt(3))^n)/2.
%F a(n) = A001075(n)+1.
%F From _R. J. Mathar_, Aug 07 2008: (Start)
%F a(n) = A102206(n-1).
%F G.f.: (1-3*x)*(x-2)/((x-1)*(x^2-4*x+1)). (End)
%F a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3). - _Wesley Ivan Hurt_, Jan 16 2024
%t Table[((-1+Sqrt[3])^n+(1+Sqrt[3])^n)^2/(2^(n+1)),{n,0,25}]
%t LinearRecurrence[{5,-5,1},{2,3,8},25] (* _Ray Chandler_, Jan 27 2014 *)
%Y Cf. A001075, A102206.
%K nonn,easy
%O 0,1
%A _Zak Seidov_, Sep 06 2006
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