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%I #22 Mar 17 2018 04:13:15
%S 2,3,7,44,494,748827,99987552,23904291912,23904291912,14647978829979,
%T 16186345621426754,45843626565163628751,235646717730827228414584,
%U 3099290829556018890177304005
%N 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.
%C 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
%e From _Andrew Howroyd_, Apr 15 2016: (Start)
%e Case n=4: There are 2 nonisomorphic symmetrical solutions (see illustration below). a(4)=(A068381(4)/8 + 2)/2 = 7.
%e __.__.__.__. __.__.__.__.
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%e Case n=5: There are 7 nonisomorphic symmetrical solutions (see illustration below). a(5)=(A068381(5)/8 + 7)/2 = 44.
%e __.__.__.__.__. __.__.__.__.__. __.__.__.__.__. __.__.__.__.__.
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%e __.__.__.__.__. __.__.__.__.__. __.__.__.__.__.
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%e (End)
%Y Cf. A068381, A068416, A068392, A265914.
%K nonn
%O 2,1
%A _R. H. Hardin_, Mar 03 2002
%E a(7)-a(15) from _Andrew Howroyd_, Apr 15 2016
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