A new homologous series of oxygen-vacancy-ordered perovskites with the formula Sr_{4+n}Mn;{3+}_4Mn;{4+}_nO_{10+3n} is proposed based on the structural trends found for the recently described Sr(4)Mn(4)O(10), Sr(5)Mn(5)O(13) and Sr(7)Mn(7)O(19) compounds. These compounds correspond to n = 0 (Sr(4)Mn;{3+}_4O(10)), n = 1 (Sr(5)Mn;{3+}_4Mn(4+)O(13)) and n = 3 (Sr(7)Mn;{3+}_4Mn;{4+}_3O(19)) members of the series. A linear set of four Mn(3+)O(5) pyramids placed on the ab plane and pointing along the +x, -y, +y, -x directions defines the n = 0 building block for the series. The nth members can be constructed from blocks containing four pyramids and n Mn(4+)O(6) octahedra with 2/m symmetry. Compounds in the related systems CaMnO(x) and LaCuO(x), containing Mn(3+) and Cu(2+) pyramids and Mn(4+) and Cu(3+) octahedra have also been found to be members of the series. The size and charge of the A-site cation and the apical distortion of the pyramidally coordinated B-site cation are shown to be important factors in the stabilization of certain members of the series. A qualitative explanation for the absence of some of the possible members of the series is presented based on these factors.