  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,... .
