
I was wondering for a longer time if this approach can be improved to handle also more dimensional linear recurrences.
For example A(x,y)=k*A(x1,y)+m*A(x,y1)+n*A(x2,y).
Suppose that A(0,x),A(x,0) are given.
Linear recurrences depending on constant last terms can be solved also by generating functions, so I tried also this method, but I do not know what to do with product of functions, for example when: f(x,y) = 1  f(x,y1)*f(x1,y).
Anyone heard about some multidimensional matrices used for this more variables recurrences? me not, but it would be great if someone had :) 