  Monogamy and polygamy relations characterize the distributions of
entanglement in multipartite systems. We investigate the monogamy and polygamy
relations with respect to any partitions for a superposition of the generalized
$W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the
R\'enyi-$\alpha$ entanglement. By using the Hamming weight of the binary
vectors related to the partitions of the subsystems, new classes of monogamy
and polygamy inequalities are derived, which are shown to be tighter than the
existing ones. Detailed examples are presented to illustrate the finer
characterization of entanglement distributions.
