A181148 Number of distinct oval-partitions of the regular 2n-gon {2n}.

1, 1, 1, 1, 3, 7, 41, 335

Offset

1,5

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}. An oval-partition is distinct if every oval in the partition is different. Here, a(n) is the number of distinct oval-partitions 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), 129-154.

A. H. Schoen, Geometry garret [see ROMBIX Supplementary Manual 1994; cached copy]

Crossrefs

Sequence A177921 gives the total number of oval-partitions of {2n}, distinct or not.

Sequence in context: A018969 A018971 A006383 * A179907 A080581 A086397

Adjacent sequences: A181145 A181146 A181147 * A181149 A181150 A181151

Keyword

nonn,more

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