(Python)
from itertools import product
def cf(s):
for l in range(1, len(s)//3+1):
for i in range(len(s) - 3*l+1):
if s[i:i+l]*2 == s[i+l:i+3*l]: return False
return True
def a(n):
if n == 0: return 1
return 4*sum(cf("0"+"".join(w)) for w in product("0123", repeat=n-1))