The stereoselective and sequence controlled coordination copolymerizations of butadiene (BD) and styrene (St) with diblock, tapered, gradient, and random sequence distributions were achieved for the first time through varying the central metals of the rare-earth metal bis(alkyl) catalyst precursors (Flu-CH2-Py)Ln(CH2SiMe3)(2)(THF)(x) (Flu = fluorenyl, Py = pyridyl, x = 1: Ln = Nd(1), Y(2), Tm(3); x = 0, Ln = Sc(4)). The thermal behavior, morphology, and the mechanical property of these copolymers were analyzed, and their relationships were established for the first time. The mechanism of central metal size tuning the sequence distribution was discussed based on DFT calculations.