A trinomial lattice is a special case of a trinomial tree. From each node three moves are possible: up, middle, and down. The special feature of the lattice is that certain pairs of moves lead to identical nodes two periods in the future. We can express these equivalences as

\[\begin{aligned}\text { up-down } & =\text { down-up }=\text { middle-middle } \\\text { middle-down } & =\text { down-middle } \\\text { middle-up } & =\text { up-middle }\end{aligned}\]

Draw a trinomial lattice spanning three periods. How many nodes does it contain? How many nodes are contained in a full trinomial tree of the same number of periods?