How could one write a closed form function of the following..F(n) = 3 * (F(n-1) – F(n-2)) + F(n-3) + 3

F(0) = 0

F(1) = 1

F(2) = 4

Computing

f(3) = 3 * (4-1) + 0 + 3 = 12

f(4) = 3 * (12-4) + 1 + 3 = 28

f(5) = 3 * (28-12) + 4 + 3 = 55

I am not seeing a pattern here any help would be appreciated.