Do you know the characteristic equation method of solving recurrences?
Rewrite the recurrence as a_n - 2a_(n-1) + a_(n-3) = 0
Characteristic equation is r^3 - 2r^2 + 1 = 0
Find all solutions for r.
You should find 3 different roots r_1, r_2, r_3.
Your final formula is a_n = A*r_1^n + B*r_2^n + C*r_3^n
Now use the initial conditions to find A, B, and C.