  Pr$_4$Ni$_3$O$_8$ is an overdoped analog of hole-doped layered cuprates. Here
we show via ab initio calculations that Ce-doped Pr$_4$Ni$_3$O$_8$
(Pr$_3$CeNi$_3$O$_8$) has the same electronic structure as the
antiferromagnetic insulating phase of parent cuprates. We find that substantial
Ce-doping should be thermodynamically stable and that other 4+ cations would
yield a similar antiferromagnetic insulating state, arguing this configuration
is robust for layered nickelates of low enough valence. The analogies with
cuprates at different $d$ fillings suggest that intermediate Ce-doping
concentrations near 1/8 should be an appropriate place to search for
superconductivity in these low-valence Ni oxides.
