Question: 2017 Winter Final - 8
Consider bitstrings that contain at least one occurrence of 000. Let $S_n$ be the number of such
strings having length $n$. Which of the following is true for $n \geq 4$?
(a)
$S_n = S_{n-1} + S_{n-2} + 2^{n-2}$
(b)
$S_n = S_{n-1} + S_{n-2} + S_{n-3}$
(c)
$S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-4}$
(d)
$S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-3}$