Revealing the size-dependent periodicities (including formula, growth pattern, and property evolution) is an important task in metal nanocluster research. However, investigation on this major issue has been complicated, as the size change is often accompanied by a structural change. Herein, with the successful determination of the Au-44(TBBT)(28) structure, where TBBT = 4-tert-butylbenzenethiolate, the missing size in the family of Au-28(TBBT)(20), Au-36(TBBT)(24), and Au-52(TBBT)(32) nanoclusters is filled, and a neat "magic series" with a unified formula of Au8n+4(TBBT)(4n+8) (n = 3-6) is identified. Such a periodicity in magic numbers is a reflection of the uniform anisotropic growth patterns in this magic series, and the n value is correlated with the number of (001) layers in the face-centered cubic lattice. The size-dependent quantum confinement nature of this magic series is further understood by empirical scaling law, classical "particle in a box" model, and the density functional theory calculations.