Done in mathematica

#$4$

What follows is called a second$-$order linear recurrence relation:

$a_n=-3a_{n-1}-2a_{n-2},n2$

$a_0=0$

$a_1=1$

Write a recursive function in Mathematica that computes values for this recursion.

According to theorems about recursions, the solution to this recursion is $a_n=2(-2{)}^{n-1}+(-1{)}^n,n0.$

Test your recursion by comparing the value of $a_{15}$ from your recursion and using the formula. Did they match?