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A373695
Number of incongruent n-sided "sporadic" Reinhardt polygons.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4392, 0, 0, 1308, 0, 0, 93, 0, 0, 0, 27, 0, 0, 0, 0, 153660, 0, 0, 315, 0, 0, 0, 0, 0, 161028, 0, 0, 0, 0
OFFSET
1,30
COMMENTS
The first nonzero entries are a(30)=3, a(42)=9, a(45)=144, a(60)=4392. It is proved that a(2^a p^b)=0, if p is an odd prime, a,b>=0. Also a(pq)=0 and a(2pq)=(2^(p-1)-1)(2^(q-1)-1)/(pq), if p and q are distinct odd primes.
LINKS
Kevin G. Hare and Michael J. Mossinghoff, Sporadic Reinhardt Polygons, Discrete & Computational Geometry. An International Journal of Mathematics and Computer Science 49, no. 3 (2013): 540-57.
Kevin G. Hare and Michael J. Mossinghoff, Most Reinhardt Polygons Are Sporadic, Geom. Dedicata 198 (2019): 1-18.
Michael J. Mossinghoff, Enumerating Isodiametric and Isoperimetric Polygons, J. Combin. Theory Ser. A 118, no. 6 (2011): 1801-15.
Michael Mossinghoff, I love Reinhardt Polygons, ICERM 2014.
FORMULA
a(n) = A374832(n) - A373694(n).
CROSSREFS
Sequence in context: A010104 A282673 A327159 * A280051 A030121 A320659
KEYWORD
nonn
AUTHOR
Bernd Mulansky, Aug 04 2024
STATUS
approved