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A309318 a(n) is the number of polygons whose vertices are the (2*n+1)-th roots of unity and whose 2*n+1 sides all have distinct slopes. 2
1, 2, 24, 180, 2700, 74184, 2062800, 81067840, 3912595776 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The polygons are counted as nonequivalent by reflection and rotation.
No even-sided polygons follow this rule.
This is the number of harmonious labelings on a cycle. See A329910 for the definition of harmonious labelings. - Wenjie Fang, Oct 14 2022
LINKS
EXAMPLE
For n=2, the a(2)=2 solutions for 2*2+1 = 5 sides are the regular pentagon and pentagram.
CROSSREFS
Cf. A001710 (number of polygons with n-1 sides), A329910.
Sequence in context: A052411 A073066 A002736 * A131972 A059387 A126190
KEYWORD
nonn,more
AUTHOR
Ludovic Schwob, Jul 23 2019
EXTENSIONS
a(7)-a(9) from Giovanni Resta, Jul 27 2019
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)