def avoids(w, pattern):

    l = [len(p) for p in pattern]

    l_p = len(pattern)

    n = len(w)

    A = sorted(list(set([a for p in pattern for a in p])))

    pattern = [[A.index(a) for a in p] for p in pattern]

    k = 1+max(max(p) for p in pattern)

​

    def is_match(s):

        assignment = [None]*k

        for i in range(l_p):

            for j in range(len(pattern[i])):

                l = w[s[i]+j]

                p = pattern[i][j]

                m = assignment[p]

                if m is None:

                    assignment[p] = l

                elif m != l:

                    return False

        return all(assignment[i] < assignment[i+1] for i in range(k-1))

    for s in Subsets(list(range(len(w))), l_p)._fast_iterator():

        if all(s[i]+l[i] <= s[i+1] for i in range(l_p-1)) and s[-1]+l[-1] <= n:

            if is_match(s):

                return False

    return True

​

def statistic(la):

    mset = [i for i, p in enumerate(la) for _ in range(p)]

    return len([w for w in Permutations(mset)if avoids(w, [[1,3,2]])])

​

​

​

parent_initializer = Compositions

element_repr = repr

levels = [2, 3, 4, 5, 6, 7]

for level in levels:

    for elt in parent_initializer(level):

        print('%s  =>  %s' % (element_repr(elt), statistic(elt)))