Valid move sequences on one axis on a 13x13x13 cube

valid-axis-seq-13.py

from itertools import product

disallow = 0
for move in product([0, 1, 2, 3], repeat=13):
        A, B, C, D = [move.count(i) for i in range(4)]
        if max(A, B, C) > D:
                disallow += 1

total = 4**13 - 1 # empty sequence
print('keep {} / {} move sequences'.format(total - disallow, total))

# output:
# keep 21281715 / 67108863 move sequences