

A181148


Number of distinct ovalpartitions of the regular 2ngon {2n}.


1




OFFSET

1,5


COMMENTS

For each n there is a list of floor{n/2} rhombs, a foursided 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 centrosymmetric polygon with 2k sides and contains k(k1)/2 rhombs. The regular 2ngon {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 ovalpartition of {2n}. An ovalpartition is distinct if every oval in the partition is different. a(n) is the number of distinct ovalpartitions of {2n}.


LINKS

Table of n, a(n) for n=1..8.
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), 129154.
A. H. Schoen, Geometry garret [see ROMBIX Supplementary Manual 1994; cached copy]


CROSSREFS

Sequence A177921 gives the total number of ovalpartitions of {2n}, distinct or not.
Sequence in context: A018969 A018971 A006383 * A179907 A080581 A086397
Adjacent sequences: A181145 A181146 A181147 * A181149 A181150 A181151


KEYWORD

nonn


AUTHOR

John P. McSorley, Jan 27 2011


EXTENSIONS

Term a(8) corrected and sequence explanation improved by John P. McSorley, Feb 26 2011


STATUS

approved



