How to prove that the Code and my mathematical formular have the same outcomes

Question

public static long hokuspokus(long n ) {
if( n > 2 ) {
return 9 ∗ hokuspokus( n − 2 ) − 16;
}
else {
return 2 ∗ n + 1 ;
}
}

now i found Out that 3^(n-1) +2 has the same results ... but i dont know how to "mathematically" prove that

i also know that 3^n - 4* (3^i + 3^n-3 ... + 3^n-2)
i =0
could someone please Help me?:)

Answer 1

You can test it with JUnit
for this you have to create a new Testclass.in eclipse you simply right click on your project, new and select Junit test case or something like that.
There you call your method with some data. But k of the magic part
if your method returns something do it like this
assertEquals(yourMethod(), desired result);
Then you run it.
If everything is all right, you will get a green bar at the left side. If not, you will get a stack trace with details

Answer 2

Google will help too. Just search for Junit testing