Chapter 6.2, Problem 66E

Let $M_n$ be the matrix with all 1‘s along the main diagonal, directly above the main diagonal, and directly below the diagonal, and 0’s everywhere else. For example,
$M_4=\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 1& 0\\ 0& 1& 1& 1\\ 0& 0& 1& 1\end{array}\right]$ .
Let $d_n=\det \left(M_n\right)$ .
a. Find a f formula expressing $d_n$ in terms of $d_{n-1}$ and $d_{n-2}$ , for positive integers $n\ge 3$ .
b. Find $d_1,d_2,\mathrm{...},d_8$ .
c. What is the relationship between $d_n$ and $d_{n+3}$ ? Whatabout $d_n$ and $d_{n+6}$ ?
d. Find $d_{100}$ .