We study the Rydberg excitation dynamics of laser-driven atoms confined in a one-dimensional three-site lattice with open boundary conditions. Different regular excitation patterns are obtained within various parameter regimes. In the case of a weak Rydberg-Rydberg interaction, the excitation probability possesses a nodal structure which is characterized by an envelope with a period inversely proportional to the interaction. For strong Rydberg interaction we observe dipole blockade and antiblockade effects and an appropriate detuning leads to an overall oscillatory behavior of the Rydberg probability density which is modulated only by small oscillations. Besides an exact diagonalization procedure we study the system by performing first and second order perturbation theory as well as a spectral analysis.