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%I #5 Mar 30 2012 17:34:20
%S 1,1,2,5,10,23,50,107,232,500,1078,2323,5007,10789,23248,50092,107934,
%T 232566,501111,1079745,2326528,5012972,10801454,23273900,50148285,
%U 108054537
%N a(n) = Floor[1/2((1-2/Sqrt[3])^n+(1-2/Sqrt[3])^n)]
%C A Binet sequence solution with ratio =(2+Sqrt[3])/Sqrt[3] ( called a trident sequence after the graphic it comes from).
%t Needs["DiscreteMath`RSolve`"]; Clear[f]; f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == 2*a[n - 1] + a[n - 2]/3, a[0] == 1, a[1] == 1}, a[n], n][[1]] // Simplify] // ToRadicals Table[Floor[N[f[n]]], {n, 0, 25}]
%K nonn
%O 0,3
%A _Roger L. Bagula_, Apr 03 2006
%E Edited by _N. J. A. Sloane_, May 04 2006
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