http://www.douban.com/people/mckelvin/status/1100048453/#last

test.py

cnt = {}
MAX_DEP = 10

def traverse(dep, i, size):
    cnt[i] = cnt.get(i, 0) + 1
    if dep >= MAX_DEP: return
    for j in range(size):
        traverse(dep + 1, i + j + 1, size + 1 - j)

traverse(0, 0, 1)

for i in range(8):
    print i, cnt[i]

traverse(dep, i, size)表示遍历深度为dep，节点值为i，子节点数为size的节点