The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181148 Number of distinct oval-partitions of the regular 2n-gon {2n}. 1
1, 1, 1, 1, 3, 7, 41, 335 (list; graph; refs; listen; history; text; internal format)



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}.


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]


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




John P. McSorley, Jan 27 2011


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)