Consider . You have :
Now
.
Solve for and express it as partial fractions; the coefficient of will be .
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.