  We present numerical evolutions of three equal-mass black holes using the
moving puncture approach. We calculate puncture initial data for three black
holes solving the constraint equations by means of a high-order multigrid
elliptic solver. Using these initial data, we show the results for three black
hole evolutions with sixth-order waveform convergence. We compare results
obtained with the BAM and AMSS-NCKU codes with previous results. The
approximate analytic solution to the Hamiltonian constraint used in previous
simulations of three black holes leads to different dynamics and waveforms. We
present some numerical experiments showing the evolution of four black holes
and the resulting gravitational waveform.
