import numpy as np

MAX_DEPTH = 61
level = np.array([1], dtype=np.uint64)

for depth in range(MAX_DEPTH + 1):
    mod3 = level % 3
    mod6 = level % 6
    branch = mod6 == 4
    branch_values = level[branch]
    mod18 = branch_values % 18

    if depth == MAX_DEPTH:
        print({
            "depth": depth,
            "nodes": int(level.size),
            "fertile": int(np.count_nonzero(mod3)),
            "sterile": int(level.size - np.count_nonzero(mod3)),
            "branch": int(branch_values.size),
            "branch_4": int(np.count_nonzero(mod18 == 4)),
            "branch_10": int(np.count_nonzero(mod18 == 10)),
            "branch_16": int(np.count_nonzero(mod18 == 16)),
        })
        break

    doubled = level * 2

    # Every branch has an odd predecessor except 4,
    # whose predecessor 1 would recreate the root cycle.
    valid_branch = branch & (level != 4)
    odd_children = ((level[valid_branch] - 1) // 3).astype(np.uint64)

    level = np.concatenate((doubled, odd_children))