  The Landau level spectra and the quantum Hall effect of ABA-stacked
multilayer graphenes are studied in the effective mass approximation. The
low-energy effective mass Hamiltonian may be partially diagonalized into an
approximate block-diagonal form, with each diagonal block contributing
parabolic bands except, in a multilayer with an odd number of layers, for an
additional block describing Dirac-like bands with a linear dispersion. We fully
include the band parameters and, taking into account the symmetry of the
lattice, we analyze their affect on the block-diagonal Hamiltonian.
Next-nearest layer couplings are shown to be particularly important in
determining the low-energy spectrum and the phase diagram of the quantum Hall
conductivity, by causing energy shifts, level anti-crossings, and valley
splitting of the low-lying Landau levels.
