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A354602
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a(n) is the number of trivial braids on 3 strands with 2*n crossings.
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1
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OFFSET
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0,2
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COMMENTS
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In other words, a(n) is the number of products of 2*n generators in the braid group B_3 which are equal to the identity element of the group.
Only braids with an even number of crossings are considered because a braid with an odd number of crossings cannot be trivial.
If we do include the 0s corresponding to the odd values of the number of crossings, a group-theoretical name for this sequence is the cogrowth sequence of B_3.
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LINKS
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CROSSREFS
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Cf. A000984 (number of trivial braids on 2 strands with 2*n crossings), A047849 (number of trivial permutations of 3 elements after 2*n adjacent transpositions).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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