#!/usr/bin/env python

uncover = {
    0 : [(1,2),(3,6),(4,8)],
    1 : [(4,7)],
    2 : [(1,0),(4,6),(5,8)],

    3 : [(4,5)],
    4 : [],
    5 : [(4,3)],

    6 : [(3,0),(4,2),(7,8)],
    7 : [(4,1)],
    8 : [(7,6),(4,0),(5,2)],
}

allpos = range(9)
cover = lambda c: [x for x in allpos if x not in c]
available = {
  0 : cover([0,2,6,8]),
  1 : cover([1,7]),
  2 : cover([0,2,6,8]),

  3 : cover([3,5]),
  4 : cover([4]),
  5 : cover([5,3]),

  6 : cover([0,2,6,8]),
  7 : cover([7,1]),
  8 : cover([0,2,6,8]),
}

def visible(path):
    last = path[-1]
    vis = list(available[last])
    for c,u in uncover[last]:
        if c in path[:-1]:
            vis.append(u)
    return vis

def nextpaths(path):
    return [path + [s] for s in visible(path) if s not in path]

def extend(paths, length):
    if length != 0:
        return extend([np for p in paths for np in nextpaths(p)], length-1)
    else:
        return paths

corner = [[0]]
side = [[1]]
middle = [[4]]

for length in range(1,9):
    print length, (  4*len(extend(corner, length))
                   + 4*len(extend(side, length))
                   + len(extend(middle, length)))