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A295264
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Number of total cyclic orders Z on {0, ..., n-1} such that (i, (i+1) mod n, (i+2) mod n) in Z for 0 <= i < n.
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3
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1, 1, 1, 1, 2, 9, 31, 128, 708, 4015, 24865, 177444, 1357830, 11141634, 99680595, 953369248, 9687797896, 104909705019, 1202985610821, 14542305462860, 185165060805578, 2476043157780478, 34673872424313463
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OFFSET
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1,5
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COMMENTS
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For all n >= 1, a(n) is the number of n-sided polygons, turning always in the same direction (right or left) while following its edges. By "n-sided polygons" we mean the polygons that can be drawn by connecting n equally spaced points on a circle. - Ludovic Schwob, Apr 04 2021
For all n >= 1, a(n) is the number of cyclic permutations of length n that avoid consecutive patterns 123, 231, and 312. - Rupert Li, Jul 27 2021
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LINKS
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PROG
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(PARI) \\ Needs B function from A343257.
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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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Corrected initial offset/terms by Rupert Li, Sep 17 2021
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STATUS
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approved
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