Techniques for Multistage A2 Lattice Structure Construction and Calculation Using Triangular Number (Tn) and Square Number (Sn)

In this paper, the connection between triangular number (T
_n
), square number (S
_n
) for construction and counting the A
₂
lattice number in lattice vector quantization is presented. We also observe that unique hexagonal A
₂
lattice can be formed from two triangular numbers (T
_n
) and a square number (S
_n
) combination. Furthermore, the number of multistage A
₂
lattice (W
_n
) is derived from A
₂
lattice number (
_L
n). Analysis of the number of lattice points produced is also presented. Thus, this analysis produces a new way to calculate the bit rate.