A373695 - OEIS

%I #20 Sep 03 2024 01:33:24

%S 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,

%T 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,

%U 0,93,0,0,0,27,0,0,0,0,153660,0,0,315,0,0,0,0,0,161028,0,0,0,0

%N Number of incongruent n-sided "sporadic" Reinhardt polygons.

%C 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.

%H Kevin G. Hare and Michael J. Mossinghoff, <a href="https://doi.org/10.1007/s00454-012-9479-">Sporadic Reinhardt Polygons</a>, Discrete & Computational Geometry. An International Journal of Mathematics and Computer Science 49, no. 3 (2013): 540-57.

%H Kevin G. Hare and Michael J. Mossinghoff, <a href="https://doi.org/10.1007/s10711-018-0326-5">Most Reinhardt Polygons Are Sporadic</a>, Geom. Dedicata 198 (2019): 1-18.

%H Michael J. Mossinghoff,  <a href="https://doi.org/10.1016/j.jcta.2011.03.004">Enumerating Isodiametric and Isoperimetric Polygons</a>, J. Combin. Theory Ser. A 118, no. 6 (2011): 1801-15.

%H Michael Mossinghoff, <a href="https://icerm.brown.edu/materials/Slides/sw-14-1/Reinhardt_Polygons_%5D_Michael_Mossinghoff.pdf">I love Reinhardt Polygons</a>, ICERM 2014.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Reinhardt_polygon">Reinhardt polygon</a>

%F a(n) = A374832(n) - A373694(n).

%Y Cf. A374832, A373694.

%K nonn

%O 1,30

%A _Bernd Mulansky_, Aug 04 2024