This problem is derived from the previous problem, Problem 5. In this problem, we consider the set of all the binary square matrices of size `n\times n`, denoted by `\mathcal B_{n,n}`. Suppose `M\in\mathcal B_{n,n}` and `P\in \mathcal B_{2,2}`, we define `mch(P,M)` as the number of occurences of `P` as blocks in `M`. If `mch(P,M)=0`, we say `M` avoids `P`.
For example, `P=[[1,1],[1,1]]\in \mathcal B_{2,2}` and `M=[[0,0,1,1],[1,0,1,1],[1,1,1,1],[1,1,1,0]]\in \mathcal B_{4,4}`.
We see `mch(P,M)=4`. Note that occurences could be overlapped. In this example, there are two occurences in the third and fourth column.
`a(n)` is the number of elements in `\mathcal B_{n,n}` avoiding `P=[[0,1],[1,1]]`.
For example, `a(1)=2`, `a(2)=15`.
Find `a(n)`.