Question 8
A binary sequence is a sequence in which each term is $0$ or $1$. A binary sequence $(a_0,a_1,\ldots,a_{n-1},a_n)$ is dyadic if it has an even number of terms and $a_0+a_n=a_1+a_{n-1}=a_2+a_{n-2}=\cdots=1$. For example, $(1,0,0,1,1,0)$ is a dyadic sequence of length $6$. How many binary sequences are there of length $16$ that are not dyadic, but are composed of $4$ consecutive dyadic sequences each of length $4$?