Distinct Reversible Primitive Binary Necklaces
Python 2, 178 171 139 137 bytes



lambda n:sum(1-any(i&gt;int(b[j::-1]+b[:j:-1],2)or j*(i&gt;=int(b[j:]+b[:j],2))for j in range(n))for i in range(2**n)for b in[bin(i+2**n)[3:]])


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