Sequentially balanced three-squares cross-over designs

Many cross-over designs with t > or = 2 treatments and periods and n = bt subjects (b an integer > or = 1) which incorporate balance for first-order carry-over effects are already known: single squares with any even value of t and some odd ones also; and sequentially balanced pairs of squares for any odd t > or = 3. We describe the construction of designs with b = 3, for t < or = 5, 7, 9, .... This permits use of sequentially balanced designs for any combination of b > 1 and t, except for b = t = 3, for which no such design exists.