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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

Table of n, a(n) for n=1..18.

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.)