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God's Algorithm out to 14q*

I've computed the count of positions out to 14 quarter turns.

First, positions at exactly the given distance:

 d  mod M + inv         mod M      positions
-- ------------ ------------- --------------
 0            1             1              1
 1            1             1             12
 2            5             5            114
 3           17            25           1068
 4          130           219          10011
 5         1031          1978          93840
 6         9393         18395         878880
 7        86183        171529        8221632
 8       802788       1601725       76843595