Help with recursion equation

I'm having problems solving

x_(n+2) - 2*x_(n+1) + x_(n) = 6  ,  n=0,1,2,...

x_0 = 3
x_1 = 0

It's always ending up with fucking 0=6 when i'm trying find a
particular solution. I'd be grateful for help.

Can't be done. I'm black.

let x_n = p^n, solve for the general solution, if you can't do that bit, you shouldn't be trying this anyway.


then the particular solution is going to be of the form an^2 + bn +c

Solve the simultaneous eqn's that result.

General solution?  Particular solution?  This isn't some Dif Eq.

This recurrence equation is a numerical approximation of the 2nd derivative of some function x.  This is a non zero constant, and is exact iff the function is a quadratic.  Thus, we already know it's 3n² + bn + c.

x₀ = 3 implies that c = 3.  Thus, 3n² + bn + 3.

x₁ = 0 then forces b = -6.

Thus, x_n = 3n² - 6n + 3.