Finding a closed form of the following

[thesandbox]

Homework Statement

Create a closed form for:
ƒ_n = 14ƒ_{n − 1} − 32ƒ_{n − 2} + 24ƒ_{n − 3}

Homework Equations

Initial conditions:
ƒ(0) = 2
ƒ(1) = 5
ƒ(2) = 11

The Attempt at a Solution

Because it's 3^rd order, it has me confused as how to start it. I was thinking something along the lines of C₁*λⁿ, C₂*λ^n-1 like you would for say, the Fibonacci Sequence, but I'm not entirely sure. What are the first few steps in solving this and the method involved?

 

[jbunniii]

What techniques do you have available? Do you know about generating functions?