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.

2, 3, 7, 44, 494, 748827, 99987552, 23904291912, 23904291912, 14647978829979, 16186345621426754, 45843626565163628751, 235646717730827228414584, 3099290829556018890177304005

Offset: 2

Author

R. H. Hardin, Mar 03 2002

Keywords

• nonn

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

Examples

			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.
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   |   __    __|   |   __   |  |
   |  |  |  |  |   |  |  |  |  |
   |__|  |__|  |   |  |  |__|  |
   |__.__.__.__|   |__|__.__.__|
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.

Extensions

a(7)-a(15) from Andrew Howroyd, Apr 15 2016