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A054761
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Number of positive braids with n crossings of 5 strands.
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2
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1, 4, 13, 37, 99, 254, 636, 1567, 3822, 9261, 22346, 53773, 129174, 309958, 743228, 1781330, 4268166, 10224885, 24492034, 58662298, 140498877, 336491169, 805872377, 1929983778, 4622083068, 11069289411, 26509431448, 63486333364
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OFFSET
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0,2
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COMMENTS
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The (n+1)-strand braid group B_{n+1} has n generators s_1,...,s_n with relations s_i s_k s_i = s_k s_i s_k for k=i+1, s_i s_k = s_k s_i for k>i+1. The elements are the isotopy classes of (n+1) free strands that are planarily "mixed" (s_i corresponds to the operation of crossing the i-th strand under the (i+1)-th strand)..
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REFERENCES
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F. A. Garside, The braid group and other groups, Quart. Journal Math. Oxford, 1969
K. Saito, Growth functions associated with Artin monoids of finite type, Proc. Japan Acad. Ser. A Math. Sci., 84 (2008), no. 10, 179--183. [From Ignat Soroko (ignat.soroko(AT)gmail.com), Sep 30 2010]
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LINKS
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Table of n, a(n) for n=0..27.
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FORMULA
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G.f.: 1/(1-4x+3x^2+3x^3-2x^4-2x^6+x^10) [From Ignat Soroko (ignat.soroko(AT)gmail.com), Sep 30 2010]
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CROSSREFS
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Cf. A000071, A054480.
Sequence in context: A003727 A103082 A048474 * A080145 A097551 A224033
Adjacent sequences: A054758 A054759 A054760 * A054762 A054763 A054764
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KEYWORD
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nonn
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AUTHOR
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Serge Burckel (burckel(AT)univ-reunion.fr), Apr 27 2000
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EXTENSIONS
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More terms from Ignat Soroko (ignat.soroko(AT)gmail.com), Sep 30 2010
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STATUS
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approved
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