Consider the sequence defined for ninN by:

a$\_(1)=1,$a$\_(2)=2,$a$\_(3)=4$

And a$\_($n$)=5$a$\_($n$-2)-2$a$\_($n$-3)$ for n$>=4.$ Prove, using strong induction, that a$\_($n$)=2^($n$-1)$ for all ninN,

Note: Make sure to carefully determine how many base cases you need and when your induction should start. Your proof should

include justification that you have enough base cases and that when you use your IA$,$ it is in the appropriate range.