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Search: id:A124723
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| A124723 |
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Number of ternary Lyndon words with exactly five 1's. |
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+0
6
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| 2, 12, 56, 224, 806, 2688, 8448, 25344, 73216, 205004, 559104, 1490944, 3899392, 10027008, 25401752, 63504384, 156893184, 383516672, 928514048, 2228433712, 5305794560, 12540968960, 29444014080, 68702699520, 159390262880
(list; graph; listen)
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OFFSET
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6,1
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FORMULA
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G.f.: 2*x^6*(1-2*x+3*x^2)*(1-x)^2/(1-2*x^5)/(1-2*x)^5= (1/(1-2*x)^5-1/(1-2*x^5))/5
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EXAMPLE
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a(7) = 12 because 11111ab, 1111a1b, 111a11b where ab = 22, 23, 32 or 33 are all ternary Lyndon words of length 7 with five 1's
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MAPLE
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(Maple) a := n -> (Matrix([[806, 224, 56, 12, 2, 0$5]]). Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [10, -40, 80, -80, 34, -20, 80, -160, 160, -64][i] else 0 fi)^(n-10))[1, 1] ; seq (a(n), n=6..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2008]
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CROSSREFS
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Cf. A051168, A027376, A124720, A124721, A124722.
Sequence in context: A038175 A025171 A127214 this_sequence A122229 A127216 A006659
Adjacent sequences: A124720 A124721 A124722 this_sequence A124724 A124725 A124726
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 05 2006
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