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A054480
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Number of different positive braids with n crossings of 4 strands.
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1
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1, 3, 8, 19, 43, 94, 202, 429, 905, 1901, 3983, 8332, 17413, 36370, 75938, 158519, 330862, 690523, 1441082, 3007369, 6275917, 13096737, 27330418, 57033206, 119016808, 248363751, 518283950, 1081551220, 2256972626, 4709831964, 9828437634, 20509899437, 42799880699
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OFFSET
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0,2
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REFERENCES
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P. Xu, Growth of the positive braids semigroups, Journal of Pure and Applied Algebra, 1992.
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LINKS
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FORMULA
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G.f.: 1/(1-3*x+x^2+2*x^3-x^6).
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EXAMPLE
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a(3) = 19 = #{111, 112, 113, 121, 122, 123, 132, 133, 211, 213, 221, 222, 223, 232, 233, 321, 322, 332, 333}.
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MATHEMATICA
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CoefficientList[Series[1/(1-3x+x^2+2x^3-x^6), {x, 0, 40}], x] (* Harvey P. Dale, Aug 01 2020 *)
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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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Serge Burckel (burckel(AT)univ-reunion.fr), Apr 26 2000
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EXTENSIONS
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STATUS
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approved
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