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Number of ways to label the cells of an m-by-n grid such that no (orthogonally) adjacent cells have adjacent labels; square array A(m,n) read by antidiagonals
1

%I #5 Sep 23 2013 13:24:56

%S 1,1,1,1,1,1,1,0,0,1,1,0,0,0,1,1,2,24,24,2,1,1,14,1660,12072,1660,14,

%T 1,1,90,160524,16595940,16595940,160524,90,1,1,646,21914632,

%U 46053512896,696497375736,46053512896,21914632,646,1

%N Number of ways to label the cells of an m-by-n grid such that no (orthogonally) adjacent cells have adjacent labels; square array A(m,n) read by antidiagonals

%e The A(2,3) = 24 valid labelings of a 2-by-3 grid are

%e 153 163 135 513 415 416

%e 426 425 462 246 263 253

%e together with their 18 reflections and rotations.

%e The square array starts:

%e 1, 1, 1, 1, 1, 1, ...

%e 1, 1, 0, 0, 2, ...

%e 1, 0, 0, 24, ...

%e 1, 0, 24, ...

%e 1, 2, ...

%e 1, ...

%Y A(1, n) = A002464(n), A(2, n) = A229430(n)

%K nonn,tabl

%O 0,17

%A _Jens Voß_, Sep 23 2013