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A235937
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Number of circular permutations with exactly one specified increasing or decreasing modular run (3-sequence), with clockwise and counterclockwise traversals not counted as distinct.
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6
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0, 0, 0, 0, 1, 2, 11, 62, 408, 3056, 25821, 242802, 2517303, 28540102, 351383192, 4669815008, 66640974977, 1016522211474, 16507095990251, 284343231536742, 5178919228252440
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OFFSET
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1,6
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COMMENTS
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Arrangements that differ only in the direction in which the cycle is traversed do not count as different.
This sequence is the same as for straight permutations of {0,1,...,n} that begin with {0,1} and end with {n-1,n} but have no increasing or decreasing 3-sequence, viz., the sequence b(0,1...n-2,n-1) in Dymáček and Lambert.
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REFERENCES
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Paul J. Campbell, Circular permutations with exactly one modular run (3-sequence), submitted to Journal of Integer Sequences
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LINKS
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EXAMPLE
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With specified sequence 123:
a(5) = 1: 12354.
a(6) = 2: 123564, 123645.
a(7) = 11: 1235476, 1235746, 1235764, 1236475, 1236574, 1236745, 1236754, 1237465, 1237546, 1237564, 1237645.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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