Automatic Generation of Generating Functions for Chromatic Polynomials   for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
  This short article, dedicated to our beloved guru Philippe FLAJOLET (1948-2011), is a case-study in computer-generated combinatorial research, where the computer, all by itself, is using the transfer-matrix method to derive (rigorously!) rational generating functions for chromatic polynomials for infinite sequences of graphs generalizing the action of taking the Cartesian product with a path of length n, n=1,2,... . 
Shalosh B. Ekhad, Jocelyn Quaintance, and Doron Zeilberger
math.CO