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
Ludovic Schwob, Table of n, a(n) for n = 1..39
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
KEYWORD
nonn
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
a(19) onwards from Ludovic Schwob, Oct 31 2022
STATUS
approved