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A346660
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Number of cyclic patterns of length n that avoid the vincular pattern 23-1-4.
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2
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1, 1, 1, 2, 5, 14, 42, 133, 442, 1537, 5583, 21165, 83707, 345324, 1485687, 6663354, 31134078, 151408319, 765462514, 4017644518, 21860398111, 123120413119, 716701884408, 4305828784896, 26661920519485, 169937265101628, 1113616036893636, 7494786443901137
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OFFSET
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0,4
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COMMENTS
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The vincular pattern 23-1-4 requires the 2 and the 3 to be adjacent.
By the trivial Wilf equivalence obtained by reversing the permutations, a(n) is also the number of cyclic patterns of length n that avoid the vincular pattern 32-4-1.
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..500
Rupert Li, Vincular Pattern Avoidance on Cyclic Permutations, arXiv:2107.12353 [math.CO], 2021.
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FORMULA
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For n >= 2, a(n) = Sum_{i=0..n-2} binomial(n-2,i) * A092920(i).
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CROSSREFS
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Cf. A025242, A047970, A092920, A346661.
Sequence in context: A340361 A308329 A202061 * A129086 A035052 A148330
Adjacent sequences: A346657 A346658 A346659 * A346661 A346662 A346663
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KEYWORD
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nonn
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AUTHOR
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Rupert Li, Aug 03 2021
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STATUS
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approved
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