Workers will construct a rectangular brick retaining wall using bricks that measure 1 unit...

Workers will construct a rectangular brick retaining wall using bricks that measure 1 unit by 2 units. The height of the finished wall will be 2 units. Acceptable walls will have no bricks that hang over the edge of another as shown next.

In how many ways may a wall be constructed using just one brick if the wall must be 2 units tall? Two bricks? Three bricks? Four bricks? Five bricks? Sketch all the patterns for the wall in each case and count them. List the numbers in the sequence formed and explain how the sequence is generated. Will a similar sequence result if the bricks used measure 1 unit by 3 units and the wall height must be 3 units? Explain.