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A022089
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Fibonacci sequence beginning 0, 6.
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5
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0, 6, 6, 12, 18, 30, 48, 78, 126, 204, 330, 534, 864, 1398, 2262, 3660, 5922, 9582, 15504, 25086, 40590, 65676, 106266, 171942, 278208, 450150, 728358, 1178508, 1906866, 3085374, 4992240, 8077614, 13069854, 21147468, 34217322, 55364790, 89582112, 144946902
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OFFSET
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0,2
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COMMENTS
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Starting with a(0)=1, a(1)=3, a(n) = the number of ternary length-2 squarefree words of length n.
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.
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LINKS
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FORMULA
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a(n) = round( (12*phi-6)/5 * phi^n) for n>3. - Thomas Baruchel, Sep 08 2004
a(n) = 6F(n) = F(n+3) + F(n+1) + F(n-4), n>3.
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MAPLE
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a:= n-> 6*(<<0|1>, <1|1>>^n)[1, 2]:
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MATHEMATICA
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a={}; b=0; c=6; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {0, 6}, 50] (* Harvey P. Dale, Dec 05 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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