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 A295264 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. 2
 1, 1, 1, 1, 2, 9, 31, 128, 708, 4015, 24865, 177444, 1357830, 11141634, 99680595, 953369248, 9687797896, 104909705019 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 LINKS Rupert Li, Vincular Pattern Avoidance on Cyclic Permutations, arXiv:2107.12353 [math.CO], 2021. Sanjay Ramassamy, Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons, arXiv:1706.03386 [math.CO], 2017. Ludovic Schwob, Illustration of a(7) and a(8) PROG (PARI) \\ Needs B function from A343257. a(n)={sum(i=1, n, B(n, i, 1))} \\ Andrew Howroyd, May 16 2021 CROSSREFS Row sums of A343257. Sequence in context: A277246 A002774 A318124 * A150905 A150906 A150907 Adjacent sequences:  A295261 A295262 A295263 * A295265 A295266 A295267 KEYWORD nonn,more AUTHOR Eric M. Schmidt, Nov 19 2017 EXTENSIONS a(12) corrected and a(13)-a(18) from Andrew Howroyd, May 15 2021 Corrected initial offset/terms by Rupert Li, Sep 17 2021 STATUS approved

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)