Question: 2018 Fall Final - 8
Let $n \geq 1$ be an integer and let $S_n$ be the number of ways in which $n$ can be written as a
sum of 2's and 4's; the order in which the 2's and 4's occur in the sum matters. For example, $S_6 =
3$, because
$$
6 = 2 + 2 + 2 = 2 + 4 = 4 + 2.
$$
Which of the following is true for any integer $n \geq 6$?
(a)
$S_n = S_{n-2} + 4 \cdot S_{n-4}$
(b)
$S_n = S_{n-2} + S_{n-4}$
(c)
$S_n = 2 \cdot S_{n-2} + S_{n-4}$
(d)
$S_n = 2 \cdot S_{n-2} + 4 \cdot S_{n-4}$