Reactions of tin and manganese in a lanthanum/nickel eutectic melt in alumina crucibles produce La11Mn13-x-yNixAlySn4-delta (0 <= x <= 3.6; 2.5 <= y = 4.9; 0.6 <= delta <= 1.1) phases with the stoichiometry dependent on the reactant ratio. These compounds crystallize in a new tetragonal structure type in space group P4/mbm, with a = 8.4197(1) A, c = 19.2414(3) A, and Z = 2 for La11Mn13-x-yNixAlySn4-delta. The structure can be viewed as an intergrowth between La6Co11Ga3-type layers and Cr5B3-type La/Sn slabs. This system represents a unique playground to study the itinerant magnetism of diluted icosahedral Mn layers. The dilution of manganese sites in the Mn/Ni/Al layer with nonmagnetic elements has a significant effect on magnetic properties, with low Mn content analogues being paramagnetic and higher Mn content analogues such as La11Mn10Al3Sn3.4 exhibiting spin-glass behavior with a freezing transition at 20 K. The lack of long-range magnetic ordering is confirmed by heat capacity and resistivity measurements.