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A116953
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a(n) = Floor[1/2((1-2/Sqrt[3])^n+(1-2/Sqrt[3])^n)]
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0
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1, 1, 2, 5, 10, 23, 50, 107, 232, 500, 1078, 2323, 5007, 10789, 23248, 50092, 107934, 232566, 501111, 1079745, 2326528, 5012972, 10801454, 23273900, 50148285, 108054537
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OFFSET
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0,3
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COMMENTS
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A Binet sequence solution with ratio =(2+Sqrt[3])/Sqrt[3] ( called a trident sequence after the graphic it comes from).
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LINKS
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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