Brute-forcing a simple combinatorical problem to verify the correctness of out solution

polc.py

def num_to_str(n):
    return "{:012b}".format(n)

def has_four(s):
    return sum(int(ch) for ch in s)==4

def no_next_to(s):
    return s.find("11")==-1

all_possible = list(filter(no_next_to, filter(has_four, map(num_to_str, range(2**12)))))
print(all_possible)
print(len(all_possible))