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Number of n X n crossword puzzles with dihedral symmetry group, for n odd. Acceptable crossword puzzles must have all words of length 3 or more, at least one word in each row and each column and be connected.
1

%I #5 Apr 07 2020 23:35:19

%S 1,2,10,45,302,3102,45795

%N Number of n X n crossword puzzles with dihedral symmetry group, for n odd. Acceptable crossword puzzles must have all words of length 3 or more, at least one word in each row and each column and be connected.

%C The number of such puzzles for an even n = 2m is equal to the number of (2m-1) X (2m-1) puzzles.

%H Marc Brodie, <a href="/A137334/a137334.txt">Mathematica program</a>

%e a(5) = 2 because, using 0's for white squares and 1's for black squares, the only two 5 X 5 puzzles with dihedral symmetry group are:

%e 00000

%e 00000

%e 00000

%e 00000

%e 00000

%e and

%e 10001

%e 00000

%e 00000

%e 00000

%e 10001

%Y Cf. A130578, A133226, A133253, A133258.

%K nonn

%O 3,2

%A Marc Brodie (mbrodie(AT)wju.edu), Apr 07 2008