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Search: id:A108600
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| A108600 |
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Number of freely braided permutations of length n; the freely braided permutations are those that avoid 3421, 4231, 4312 and 4321. |
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4
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| 1, 2, 6, 20, 71, 260, 971, 3674, 14032, 53968, 208692, 810492, 3158760, 12346628, 48377494, 189952216, 747180999, 2943648824, 11612917815, 45869337526, 181372345723, 717856746216, 2843678131629, 11273602645942, 44725291921541
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OFFSET
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1,2
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REFERENCES
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R. M. Green and J. Losonczy, Freely braided elements of Coxeter groups, Ann. Comb. 6 (2002), 337-348.
T. Mansour, On an open problem of Green and Losonczy: exact enumeration of freely braided permutations, Discrete Math. Comput. Sci. 6 (2004), 461-470.
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LINKS
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V. Vatter, Enumeration scheme for freely braided permutations.
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FORMULA
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(1-3*x-2*x^2+(1+x)*sqrt(1-4*x)) / (1-4*x-x^2+(1-x^2)*sqrt(1-4*x))
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EXAMPLE
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a(5)=71 because there are 71 permutations of length 5 that avoid 3421, 4231, 4312 and 4321.
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CROSSREFS
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Sequence in context: A145138 A000707 A129777 this_sequence A128729 A006027 A049124
Adjacent sequences: A108597 A108598 A108599 this_sequence A108601 A108602 A108603
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KEYWORD
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easy,nonn
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AUTHOR
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Vince Vatter (vatter(AT)math.rutgers.edu), Jun 11 2005
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