Abracadabra!

[Taken from Schoenfeld p. 268-9 with additions by Stephanie Wilcox.]

Consider the following magical configuration. In how many ways can you read the word "ABRACADABRA?"

     A
    B B
   R R R
  A A A A
 C C C C C
A A A A A A
 D D D D D
  A A A A
   B B B
    R R
     A

Is this similar to any problems we have done before? If so, which ones and how is it similar to the other problems? Is there a way to mathematically figure this problem without working it out by hand?