See https://twitter.com/robinhouston/status/1297221537448198145

x.py

import math

TABLE = {
    (0, +1): (+1, True),   # ()
    (1, +1): (-1, False),  # (0 1 2)
    (2, +1): (-1, True),   # (0 2 1)
    (0, -1): (+1, False),  # (0 1)
    (1, -1): (-1, True),   # (1 2)
    (2, -1): (+1, True)    # (0 2)
}

def compose(tr1, tr2):
    (t1, r1), (t2, r2) = tr1, tr2
    return (t1 + r1*t2, r1*r2)

def subst(x, y):
    z = {}
    for ((t0, r0), n0) in x.items():
        # Let tr1 be the dequoted version of (t0, r0)
        t1 = (-t0) // 3
        r1, should_substitute = TABLE[t0 % 3, r0]
        tr1 = (t1, r1)

        # and substitute where appropriate
        if should_substitute:
            for (tr2, n2) in y.items():
                tr3 = compose(tr1, tr2)
                z[tr3] = z.get(tr3, 0) + n0 * n2
        else:
            z[tr1] = z.get(tr1, 0) + n0

    return z

x = { (-1, +1): 1, (0, +1): 1, (+1, +1): 1 }
print(sum(x.values()))
for i in range(10):
    x = subst(x, x)
    print(sum(x.values()))