Some notes on the numeration of the slice and anti-slice
groups....

        Analysis of the 3x3x3 Slice & Anti-Slice Groups
        -----------------------------------------------
                  arrangements           arrangements
Moves Deep     (2q or slice moves)   (4q or double slice moves)

0                    1                      1
1                    6                      9
2                   27                     51
3                  120                    247
4                  287                    428
5                  258                     32
6                   69                    ---
                   ---                    768
                   768

                  arrangements           arrangements
Moves Deep   (2q or anti-slice moves)   (4q or double anti-slice moves)

0                   1                     1
1                   6                     9
2                  27                    51
3                 120                   265
4                 423                   864
5               1,098                 1,785
6               1,770                 2,017
7               1,650                 1,008
8                 851                   144
9                 198
                -----
                6,144