Say I have the following recursive numbersequence: a(n) = a(n-1)+2a(n-2)
I know that a(1) = 2 and I know that a(2) = 3. Now I need to find an explicit formula for that.
I know it has something to do with fibonaccis sequence since, if a(1)=1 and a(2) = 1 the explicit formula would have been a(n) = (2^n-(-1)^n)/3. The problem that this does not work when a(1) = 2 and a(2) = 3.
Can anybody explain how I should come up with an explicit formula for this problem?