Given a number n$,$ consider all $2^$n sequences of a$$s and b$$s that have length n$.$ A sequence is called a good one if and only if there are no two b$$s in a row $($i$.$e$.,$ no two consecutive b$$s$)$ anywhere in it$.$ You have to count the total number N $($n$)$ of good sequences of length n$.$ Implement an algorithm to solve this problem that runs in O$($n$).$ Explain why your algorithm yields the correct solution.

For example, if n $=4,$ the following sequences are good: aaaa, aaab, aaba, abaa, baaa, abab, baab, baba : which yields the answer N $(4)=8.$ Note, that you do not need to print all good sequences; the only thing you have to do is to find the number N $($n$).$