When the sum of the aperiodic autocorrelation functions of two sequences is an impulse function, these two sequences form a Golay pair, and each sequence is a Golay sequence. Golay sequences have been used for synchronization, channel estimation, and peak-to-average power ratio reduction of multicarrier signals. The existence of Golay sequences has expanded from power of two length BPSK Golay sequences to QPSK and QAM Golay sequences whose lengths can be odd. The sequence lengths can be further extended through recursive construction. The recursive construction combines two shorter input Golay pairs into a longer output Golay pair. The alphabet and length of the output Golay pair is determined by the alphabets and lengths of the input Golay pairs. As new complex Golay sequences are continuously being discovered, the lengths where Golay sequence exist also increase continuously. However, there is no simple mathematical formula to describe all possible lengths of complex Golay sequences. In this research, a program “gseq” is created. Given a target sequence length L, this program factors the length and decide whether it is possible to recursively construct a Golay pair of length L using BPSK, QPSK, or 16-QAM input Golay pairs. Characteristics of the length and alphabet size of recursively constructed output Golay pairs are also discussed. The alphabet size will increase when the output Golay pair is formed by at least two 16-QAM input Golay pairs. The alphabet size of the recursively constructed output Golay pair with p 16-QAM input Golay pairs is analyzed. The use of reduced alphabet 16-QAM input Golay pairs is shown to effectively reduce the growth of the alphabet size of the output Golay pair.