A177921 Number of oval-partitions of the regular 2n-gon {2n}.

1, 1, 2, 4, 12, 58

Offset

1,3

Comments

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}.

Links

Table of n, a(n) for n=1..6.

John P. McSorley and Alan H. Schoen, Rhombic tilings of (n, k)-ovals, (n, k, lambda)-cyclic difference sets, and related topics, Discrete Math., 313 (2013), 129-154. - From N. J. A. Sloane, Nov 26 2012

A. H. Schoen, See ROMBIX Supplementary Manual 1994

Crossrefs

Sequence A181148 gives the total number of distinct oval-partitions of {2n}.

Sequence in context: A099928 A363005 A000568 * A301481 A128648 A128646

Adjacent sequences: A177918 A177919 A177920 * A177922 A177923 A177924

Keyword

nonn,more

Author

John P. McSorley, Dec 15 2010

Extensions

Website reference updated by John P. McSorley

Status

approved