Math Help - Magic Combinations

1. Magic Combinations

How many ways are there of spelling out “ABRACADABRA” by traversing the following diamond, always going from one letter to an adjacent one? (ignore the underscores, theyre just there to make it look like a diamond)

_____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

2. Originally Posted by aquafina
how many ways are there of spelling out “abracadabra” by traversing the following diamond, always going from one letter to an adjacent one? (ignore the underscores, theyre just there to make it look like a diamond)

_____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
If by "ways of spelling out abracadaba" you mean the number of paths from the top of the diamond to the bottom, the answer is 252.

Code:
              1
1    1
1     2    1
1     3    3     1
1     4     6    4     1
1    5    10    10    5    1
6    15    20    15    6
21    35    35    21
56    70    56
126   126
252
Do you see why?