A closed form solution of a discrete correlated random walk

A closed form solution of a discrete correlated random walk corresponding to the system of partial difference equations, L(x,t+1) = cL(x+1, t) + sR(x + 1, t) R(x, t+1) = sL(x - 1, t) + cR(x - -1, t) which can be used to model the movement of organisms on a linear path that have a preferential direction of movement will be found using Green's function techniques and combinatorial arguments.