This problem is about numbers of tilings of a grid by polyominoes.
`a(n)` is the number of tilings of a `3\times n` grid by `n` monominoes and `n` dominoes.
`b(n)` is the number of tilings of a `5\times n` grid by `n` dominoes and `n` straight trominoes.
Obviously, `a(1)=b(1)=2`. `a(2)=11` and they are in pictured in following figure.
Find `a(n)` and `b(n)`.