Flush means that two tiles have an edge in common.
From Jon Perry, May 03 2013: (Start)
If we require all tiles to be flush to each other, then the sequence is 1, 1, 2, 6, 0, 0, .... with a(n)=0 for n>=4.
The 6 patterns for n=3 are:
xxx xxx xxx oxxx +xxx xxx
oo+ o+ o+ o+ oo oo+
A proof for a(n)=0 for n>=4 is that these 6 patterns represent all possible 'hinge' patterns for any set of tiles, and by observation no 4th tile is admissible. (end)