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 A068393 Number of partitions of n X n checkerboard by two edgewise-connected sets which produce the maximum n^2-2n+2 frontier edges between the two sets. Partitions equal under rotation or reflection are counted only once. 3
 2, 3, 7, 44, 494, 748827, 99987552, 23904291912, 23904291912, 14647978829979, 16186345621426754, 45843626565163628751, 235646717730827228414584, 3099290829556018890177304005 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For even n > 2 the only symmetry possible is rotation by 180 degrees. For odd n > 1 the only symmetries are reflections either horizontally or vertically. - Andrew Howroyd, Apr 15 2016 LINKS Table of n, a(n) for n=2..15. EXAMPLE From Andrew Howroyd, Apr 15 2016: (Start) Case n=4: There are 2 nonisomorphic symmetrical solutions (see illustration below). a(4)=(A068381(4)/8 + 2)/2 = 7. __.__.__.__. __.__.__.__. | __ __| | __ | | | | | | | | | | | | |__| |__| | | | |__| | |__.__.__.__| |__|__.__.__| Case n=5: There are 7 nonisomorphic symmetrical solutions (see illustration below). a(5)=(A068381(5)/8 + 7)/2 = 44. __.__.__.__.__. __.__.__.__.__. __.__.__.__.__. __.__.__.__.__. | __| |__ | | __| |__ | | |__ __| | | | __ | | | |__ __| | | | __ | | | __| |__ | | | | | | | | __| |__ | | | | | | | | | __ | | | | | | | | | |__.__.__| | | |__| |__| | | |__| |__| | | |__| |__| | |__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__| __.__.__.__.__. __.__.__.__.__. __.__.__.__.__. |__.__ __.__| |__ __ __| | __ __ | | __| |__ | | | | | | | |__| | | |__| | | __ | | | | | | | | | __| |__ | | |__| |__| | | |__| |__| | | |__.__.__| | |__.__.__.__.__| |__.__.__.__.__| |__.__.__.__.__| (End) CROSSREFS Cf. A068381, A068416, A068392, A265914. Sequence in context: A267507 A344561 A014546 * A032053 A343522 A086542 Adjacent sequences: A068390 A068391 A068392 * A068394 A068395 A068396 KEYWORD nonn AUTHOR R. H. Hardin, Mar 03 2002 EXTENSIONS a(7)-a(15) from Andrew Howroyd, Apr 15 2016 STATUS approved

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Last modified April 25 10:01 EDT 2024. Contains 371967 sequences. (Running on oeis4.)