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.