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Search: id:A022089
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| A022089 |
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Fibonacci sequence beginning 0 6. |
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+0
3
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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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Tanya Khovanova, Recursive Sequences
C. Richard and U. Grimm, On the entropy and letter frequencies of ternary square-free words
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FORMULA
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a(n) = round( (12phi-6)/5 phi^n) (works for n>3) - Thomas Baruchel, Sep 08 2004
a(n) = 6F(n) = F(n+3) + F(n+1) + F(n-4), n>3.
a(n) = A119457(n+4,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2006
G.f.: 6x/(1-x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
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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 Orlovsky, Jul 23 2008)
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CROSSREFS
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Sequence in context: A046625 A029682 A014201 this_sequence A110357 A091827 A160729
Adjacent sequences: A022086 A022087 A022088 this_sequence A022090 A022091 A022092
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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