I am trying to understand how do you solve non homogenous recurrence relations.
So , for example, consider the following equation, $$(A-2)^2(A-1)g = 3(n^2)(2^n) + (2^n)$$ So , $A$ being the advancement operator. In general , $A$ just takes the value and use recurrence to get you to the next value in the series. $g$ being the function to be found.
What's the generalized approach to solve these kind of problems ? Googling around upto first ten results tell you the solution but not do a good job of tell the algorithm to solve this .