Your Brick-Wall company wants to produce a catalogue of designs to show to customers. If they miss out on a design then a competitor may offer it. So your company had better include all the designs you can. The brick walls are to be two units tall. The bricks are all the same size, 2 units by 1 unit.

How many different ways can you make a wall using

     1. one brick?
        Hint: There is only 1 possible pattern.
     2. two bricks?
        Hint: There are 2 possible patterns.
     3. three bricks?
        Hint: There are 3 possible patterns.
     4. four bricks?

     5. five bricks?

     6. six bricks?

     ...

     7. any number of bricks?