Putative global minima for Ga+N clusters with size ``N'' ranging from 49 to 70 are found by employing the Kohn-Sham formulation of the density functional theory, and their evolution is described and discussed in detail. We have discovered a unique growth pattern in these clusters, all of which are hollow core-shell structures. They evolve with size from one spherical core-shell to the next spherical core-shell structure mediated by prolate geometries, with an increase in overall diameter of the core, as well as the shell, without putting on new layers of atoms. We also present a complete picture of bonding in gallium clusters by critically analyzing the molecular orbitals, the electron localization function, and Bader charges. Bonding in these clusters is a mixture of metallic and covalent type that leans towards covalency, accompanied by marginal charge transfer from the surface to the core. Most molecular orbitals of Ga clusters are non-jellium type. Covalency of bonding is supported by a wide localization window of electron localization function, and joining of its basins along the bonds. (C) 2014 AIP Publishing LLC.