|
%I #30 Jun 06 2019 02:41:42
%S 1,1,2,4,12,58
%N Number of oval-partitions of the regular 2n-gon {2n}.
%C For each n there is a list of floor(n/2) rhombs, a four sided parallelogram with principal index a number from {1, 2, ..., floor(n/2)}. Such rhombs can tile an (n, k)-oval. An (n, k)-oval is a centro-symmetric polygon with 2k sides and contains k(k-1)/2 rhombs. The regular 2n-gon {2n} with 2n sides is an (n,n)-oval. Its rhombs can be partitioned into (n, k)-ovals for various values of k. This partition is called an oval-partition of {2n}. Here, a(n) is the number of oval-partitions of {2n}.
%H John P. McSorley and Alan H. Schoen, <a href="http://dx.doi.org/10.1016/j.disc.2012.08.021">Rhombic tilings of (n, k)-ovals, (n, k, lambda)-cyclic difference sets, and related topics</a>, Discrete Math., 313 (2013), 129-154. - From _N. J. A. Sloane_, Nov 26 2012
%H A. H. Schoen, <a href="http://schoengeometry.com/">See ROMBIX Supplementary Manual 1994</a>
%Y Sequence A181148 gives the total number of distinct oval-partitions of {2n}.
%K nonn,more
%O 1,3
%A _John P. McSorley_, Dec 15 2010
%E Website reference updated by _John P. McSorley_
|
