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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. 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



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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.