The series of nickel-oxide compounds LaNiO 3 (formal Ni(d 7 )), La 2 NiO 4 (formal Ni(d 8 )) and LaNiO 2 (formal Ni(d 9 )) is investigated by firstprinciples many-body, using a combination of density functional theory, selfinteraction correction and dynamical mean-field theory. The characteristics of these different nickelates, in good agreement with available experimental data, is revealed by employing a compound-independent choice for the local Coulomb interactions. The dichotomy within the low-energy dominant Ni-eg sector of {d z 2 , d x 2 −y 2 } kind is rising with growing Ni(3d) filling across the series. An intermediate-coupling scheme for spin-polarized calculations is introduced, which leads to very weak Ni ordered moments for the infinite-layer compound LaNiO 2 in contrast to the robust-moment system La 2 NiO 4 .