3x3 <r2,U,D> gods algorithm QTM

depth   states
0       1
1       4
2       7
3       12
4       29
5       60
6       108
7       220
8       463
9       888
10      1717
11      3484
12      6801
13      13036
14      25647
15      50656
16      97861
17      188828
18      367548
19      710428
20      1356064
21      2583556
22      4900746
23      9172900
24      16938473
25      30729828
26      54097248
27      91647518
28      147292074
29      215904126
30      277106513
31      301012822
32      255070009
33      149024154
34      54291014
35      11752406
36      1296665
37      56012
38      2167
39      246
40      37
41      12
42      7
43      4
44      1
45      0