How to get the characteristic equation? In my book, this succession defined by recurrence is presented:
$$U_n=3U_{n-1}-U_{n-3}$$
And it says that the characteristic equation of such is:
$$x^3=3x^2-1$$
Honestly, I don't understand how. How do I get the characteristic equation given a succession? 

"Guess" that $U(n) = x^n$ is a solution and plug into the recurrence relation:
$$
x^n = 3x^{n-1} - x^{n-3}
$$
Divide both sides by $x^{n-3}$, assuming $x \ne 0$:
$$
x^3 = 3x^2 - 1
$$
Which is the characteristic equation you have.
