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A177921 Number of oval-partitions of the regular 2n-gon {2n}. 1
1, 1, 2, 4, 12, 58 (list; graph; refs; listen; history; text; internal format)
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}. 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, On k-Ovals and (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: A020106 A099928 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

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)