  We consider planar lattice walks that start from a prescribed position, take
their steps in a given finite subset of Z^2, and always stay in the quadrant x
>= 0, y >= 0. We first give a criterion which guarantees that the length
generating function of these walks is D-finite, that is, satisfies a linear
differential equation with polynomial coefficients. This criterion applies,
among others, to the ordinary square lattice walks. Then, we prove that walks
that start from (1,1), take their steps in {(2,-1), (-1,2)} and stay in the
first quadrant have a non-D-finite generating function. Our proof relies on a
functional equation satisfied by this generating function, and on elementary
complex analysis.
