Counting Stacked Polyhexes

Since each solid hexagon has 8 faces the number of stacked hexagons is rising faster then the number of polycubes. You can check the number of stacked tetrahexes by hand, but it seems to be difficult to count pieces with more hexagons without a computer. My rather static program written in the last century produced the following numbers. In 2001 Brendan Owen counted 60020 stacked polyhexes with 8 hexagons.

n 1234 5 6 7
Number of Stacked Polyhexes 125231239117134
Number of Flat Polyhexes 11372282333
Number of Polycubes 1128291661023