What is the general form of the particular solution guaranteed to exist by Theorem 6 of the linear nonhomogeneous recurrence relation $a_{n} = 8a_{n-2} - 16a_{n-4} + F(n)$ if
- $F(n) = n^{3}?$
- $F(n) = (-2)^{n}?$
- $F(n) = n2^{n}? $
- $F(n) = n^{2}4^{n}?$
- $F(n) = (n^{2} - 2)(-2)^{n}?$
- $F(n) = n^{4}2^{n}?$
- $F(n) = 2?$
