Only if you want to count the number of different possible TM behaviours. The official count of BB TMs as given in OEIS sequence A052200 ignores such symmetries

Only if you want to count the number of different possible TM behaviours. The official count of BB TMs as given in OEIS sequence A052200 ignores such symmetries. [1] https://oeis.org/A052200 https://oeis.org/A052200