A three-stage padding configuration providing a larger continuous virtual aperture and achieving more degrees-of-freedom (DOFs) for the direction-of-arrival (DOA) estimation is presented. The improvement is realized by appropriately cascading three-stages of an identical inter-element spacing. Each stage advantageously exhibits a continuous virtual array, which subsequently produces a hole-free resulting uniform linear array. The geometrical approach remains applicable for any existing sparse array structures with a hole-free coarray, as well as designed in the future. In addition to enlarging the continuous virtual aperture and DOFs, the proposed design offers flexibility so that it can be realized for any given number of antennas. Moreover, a special padding configuration is demonstrated, which further increases the number of continuous virtual sensors. The precise antenna locations and the number of continuous virtual positions are benefited from the closed-form expressions. Experimental works are carried out to demonstrate the effectiveness of the proposed configuration.