How to find the number of nested lists in a list?

You can use a recursive function as following:

In [14]: def count_lists(l):
    ...:     return sum(1 + count_lists(i) for i in l if isinstance(i,list))
    ...: 

In [15]: 

In [15]: x=[1,2,[[[]]],[[]],3,4,[1,2,3,4,[[]] ] ]

In [16]: count_lists(x)
Out[16]: 8

This seems to do the job:

def count_list(l):
    count = 0
    for e in l:
        if isinstance(e, list):
            count = count + 1 + count_list(e)
    return count