A229429 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, 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, 1, 1, 90, 160524, 16595940, 16595940, 160524, 90, 1, 1, 646, 21914632, 46053512896, 696497375736, 46053512896, 21914632, 646, 1
Offset: 0
Examples
The A(2,3) = 24 valid labelings of a 2-by-3 grid are 153 163 135 513 415 416 426 425 462 246 263 253 together with their 18 reflections and rotations. The square array starts: 1, 1, 1, 1, 1, 1, ... 1, 1, 0, 0, 2, ... 1, 0, 0, 24, ... 1, 0, 24, ... 1, 2, ... 1, ...