It's originally derived from the pascal triangle, you know this thing

     1
    1 1
   1 2 1
  1 3 3 1
 1 4 6 4 1

if we take only bit 0, (2**0) we get this

       1
      1 1
     1 0 1
    1 1 1 1 
   1 0 0 0 1
  1 1 0 0 1 1
 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1

add up each row and we get this series

1, 2, 2, 4, 2, 4, 4, 8, ...

after thinking about it for a few minutes i realised how to generate that series
start with a list @a = (1);

#my code does this all in d() with a push and a map, ain't perl grand
1. take list @a and produce a copy of it in @d
2. double all the values in @d
3. push @b onto @a
4. goto step 1

this will produce the series above now we add all the values in the list to those before the current value (not recursively, just a simple cumulative sum) and we get

1, 3, 5, 9, 11, 15, 19, 27, ...

this is @b in my program, if you look closely at 2**$n-1 we now have 3**$n.
what i'm having a little trouble understanding is why does this produce powers of three from doubling numbers (and adding them together), maybe someone with a math degree can tell me why, also i don't know for sure that it will always give powers of 3. But i've tested it up do 24 on my computer (that used about 150MB of ram, i haven't tried higher yet)