

A295264


Number of total cyclic orders Z on {0, ..., n1} 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
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OFFSET

1,5


COMMENTS

For all n >= 1, a(n) is the number of nsided polygons, turning always in the same direction (right or left) while following its edges. By "nsided 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



