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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}. Here, a(n) is the number of oval-partitions of {2n}. LINKS 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. - 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 August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)