OFFSET
0,3
COMMENTS
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+
o o
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)
LINKS
Giovanni Resta, Illustration of a(3)
EXAMPLE
For n=2 we have:
+
+oo oo
For n=3 some examples are:
+ o+ o o
oo o o o+
xxx xxx xxx+ xxx
To calculate a(3) we use the 9 basic patterns:
o o
o o oo oo o
xxx xxx xxx xxx oxxx ooxxx
11 6 9 10 11 7
+ +
xxx xxx +xxx
5 2 4
and calculate the number of valid positions for the 1*1 tile (top row) and for the 1*2 tile (bottom row).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jon Perry, Feb 16 2013
EXTENSIONS
a(4) from Giovanni Resta, Feb 21 2013
a(5) from Giovanni Resta, Mar 12 2013
STATUS
approved