Question: 2017 Fall Final - 9
Consider bitstrings that do not contain 110. Let $S_n$ be the number of such strings having length
$n$. Which of the following is true for any $n \geq 4$?
(a)
$S_n = S_{n-1} + S_{n-2} + S_{n-3}$
(b)
$S_n = S_{n-1} + S_{n-2} + 1$
(c)
$S_n = S_{n-1} + S_{n-2} + 2^{n-2}$
(d)
$S_n = S_{n-1} + S_{n-2} + 2^{n-3}$