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EXAMPLE
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A(2,2) = 22: [(2,2),(1,1),(0,0)], [(2,2),(1,1),(0,1),(0,0)], [(2,2),(1,1),(1,0),(0,0)], [(2,2),(0,0)], [(2,2),(1,2),(0,1),(0,0)], [(2,2),(1,2),(0,2),(0,1),(0,0)], [(2,2),(1,2),(0,2),(0,0)], [(2,2),(1,2),(1,1),(0,0)], [(2,2),(1,2),(1,1),(0,1),(0,0)], [(2,2),(1,2),(1,1),(1,0),(0,0)], [(2,2),(1,2),(1,0),(0,0)], [(2,2),(0,2),(0,1),(0,0)], [(2,2),(0,2),(0,0)], [(2,2),(2,1),(1,0),(0,0)], [(2,2),(2,1),(1,1),(0,0)], [(2,2),(2,1),(1,1),(0,1),(0,0)], [(2,2),(2,1),(1,1),(1,0),(0,0)], [(2,2),(2,1),(0,1),(0,0)], [(2,2),(2,1),(2,0),(1,0),(0,0)], [(2,2),(2,1),(2,0),(0,0)], [(2,2),(2,0),(1,0),(0,0)], [(2,2),(2,0),(0,0)].
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 3, 7, 25, 121, ...
1, 2, 22, 248, 6506, 292442, ...
1, 4, 188, 11380, 2359348, 1088626684, ...
1, 8, 1712, 577124, 991365512, 4943064622568, ...
1, 16, 16098, 30970588, 453530591824, 25162900228200976, ...
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