A linear nonhomogeneous recurrence relation of degree k with constant coefficients is a recurrence relation of the form: $ a_n= c_1 a_{n-1}+c_2 a_{n-2}+\ldots+c_ka_{n-k}+f(n)$ where $c_1,c_2,\ldots,c_k$ are real numbers and $f(n)$ is a function not identically zero depending only on n.
I wonder that if $f(n)$ is an arbitrary function then all recurrent relation is a linear nonhomogeneous recurrence relation? For example, if $a_n=a_{n-1} +a_{n-2}^2$ we can definite $f(n)=a_{n-2}^2$