God's Algorithm out to 18q*: 368,071,526,203,620,348

Almost exactly four years after 17q* was announced by Thomas
Schuenemann, we have calculated the number of positions at a distance
of exactly 18 in the quarter-turn metric. This is more than one in
twenty positions.

This number matches (mod 48) the count of distance-18 symmetric
positions; this provides a bit of confirmation that it is correct
(or rather, about 5.6 bits of confirmation).

The approach we used does not permit us to calculate the number of
positions mod M or mod M+inv without significantly increasing the
amount of CPU required; these computations will have to wait for
someone with more ambition and more CPU time, or a different approach.

This new result is a part of our ongoing investigation into the
quarter-turn metric to complement the earlier work on the half-turn
metric. The bulk of the code is the same between this work and
that work, but some improvements have been made to search.

This work was supported in part by an allocation of computing time
from the Ohio Supercomputer Center.