In green wireless communication, the wireless network is preferred to design a system for low power consumption to minimize the environmental impacts of devices. An antenna is an essential tool in the transceiver system. In a multi-user network environment, large antenna arrays are required that consume high power. This paper proposes a solution using a thinned array antenna (TAA) to minimize energy use by the antenna module. For the array thinning, linear mathematical sequences like the prime number sequence and the Fibonacci sequence are used instead of conventional optimization methods. The antennas are arranged according to these sequences, and the performances are compared with the corresponding fully populated arrays. For a thinned array of 51 elements, using the prime number sequence 36.58% power saving is achieved. For a thinned array of 34 elements, using the Fibonacci sequence 26.5% power saving is achieved. The mathematical sequences (the array sequences) are directly inserted in the program of array thinning. This method doesn’t need any optimization algorithm for array thinning and hardware to implement it. The power consumption in hardware can be avoided. Therefore, the proposed thinned array antenna design using mathematical sequences provides a low-power antenna system for green wireless communication.