Pasted

>>> list(filter(is_symmetric, all_relations(3)))
[set(), {(2, 2)}, {(1, 2), (2, 1)}, {(1, 2), (2, 1), (2, 2)}, {(1, 1)}, {(1, 1), (2, 2)}, {(1, 1), (1, 2), (2, 1)}, {(1, 1), (1, 2), (2, 1), (2, 2)}, {(0, 2), (2, 0)}, {(0, 2), (2, 0), (2, 2)}, {(0, 2), (1, 2), (2, 0), (2, 1)}, {(1, 2), (2, 1), (2, 0), (0, 2), (2, 2)}, {(1, 1), (0, 2), (2, 0)}, {(1, 1), (0, 2), (2, 0), (2, 2)}, {(1, 2), (2, 1), (1, 1), (2, 0), (0, 2)}, {(1, 2), (2, 1), (1, 1), (2, 0), (0, 2), (2, 2)}, {(0, 1), (1, 0)}, {(0, 1), (1, 0), (2, 2)}, {(0, 1), (1, 0), (1, 2), (2, 1)}, {(0, 1), (1, 2), (2, 1), (2, 2), (1, 0)}, {(0, 1), (1, 0), (1, 1)}, {(0, 1), (1, 0), (1, 1), (2, 2)}, {(0, 1), (1, 2), (2, 1), (1, 1), (1, 0)}, {(0, 1), (1, 2), (2, 1), (1, 1), (2, 2), (1, 0)}, {(0, 1), (1, 0), (0, 2), (2, 0)}, {(0, 1), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (2, 0), (0, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (1, 1), (2, 0), (0, 2), (1, 0)}, {(0, 1), (1, 1), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (1, 1), (2, 0), (0, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (1, 1), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 0)}, {(2, 2), (0, 0)}, {(1, 2), (2, 1), (0, 0)}, {(1, 2), (2, 2), (2, 1), (0, 0)}, {(1, 1), (0, 0)}, {(1, 1), (2, 2), (0, 0)}, {(1, 1), (1, 2), (2, 1), (0, 0)}, {(1, 2), (2, 1), (0, 0), (1, 1), (2, 2)}, {(0, 2), (2, 0), (0, 0)}, {(2, 2), (0, 2), (2, 0), (0, 0)}, {(1, 2), (2, 1), (0, 0), (2, 0), (0, 2)}, {(1, 2), (2, 1), (0, 0), (2, 0), (0, 2), (2, 2)}, {(1, 1), (0, 2), (2, 0), (0, 0)}, {(0, 0), (1, 1), (2, 0), (0, 2), (2, 2)}, {(1, 2), (2, 1), (0, 0), (1, 1), (2, 0), (0, 2)}, {(1, 2), (2, 1), (0, 0), (1, 1), (2, 0), (0, 2), (2, 2)}, {(0, 1), (1, 0), (0, 0)}, {(0, 1), (1, 0), (2, 2), (0, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (2, 2), (1, 0)}, {(0, 1), (1, 0), (1, 1), (0, 0)}, {(0, 1), (0, 0), (1, 1), (2, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (1, 1), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (1, 1), (2, 2), (1, 0)}, {(0, 1), (0, 0), (2, 0), (0, 2), (1, 0)}, {(0, 1), (0, 0), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (2, 0), (0, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (0, 0), (1, 1), (2, 0), (0, 2), (1, 0)}, {(0, 1), (0, 0), (1, 1), (2, 0), (0, 2), (2, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (1, 1), (2, 0), (0, 2), (1, 0)}, {(0, 1), (1, 2), (2, 1), (0, 0), (1, 1), (2, 0), (0, 2), (2, 2), (1, 0)}]
>>> len(_)
64