(Solved): discrete mathematics. please provide all solutions Find all solutions of the recurrence relation \( ...

Find all solutions of the recurrence relation \( a_{n}=7 a_{n-1}-16 a_{n-2}+12 a_{n-3}+n 4^{n} \) with \( a_{0}=-2, a_{1}=0 \), and \( a_{2}=5 \) Determine whether the relations \( R_{1}, R_{2} \), and \( R_{3} \) on the set of all non-zero integers are equivalence relations, where: (a) \( (x, y) \in R_{1} \) if and only if \( x \geq y^{2} \). (b) \( (x, y) \in R_{2} \) if and only if \( x \) is a multiple of \( y \). (c) \( (x, y) \in R_{3} \) if and only if \( x y \geq 1 \).