Each object exhibits particular sequences, so perhaps those possible sequences should be included in object representation somehow.
Since L5 TT cells receive direct sensory input and form minicolumns, perhaps a subset of cells in each minicolumn belong to each object, and those cells respond to all sequences which make sense for the object. That way, it can use sequences to help recognize the object, and potentially generate behavioral sequences based on the object.
A random set of cells in each minicolumn could be assigned to each object, or some other way of forming object context, but it must track the sequence independently for each possible object. How the sequence will progress depends on the object, even if the same first part of the sequence happens to occur on two different objects, which is likely because a lot of objects share features like flat surfaces. As it narrows the possible objects down, it eliminates possible sequences.
To track sequences independently for each possible object, predictive connections can be limited to cells which belong to the same object.