OFFSET
1,2
COMMENTS
The number of compositions of the n X n grid graph is the number of partitions of an n X n square into regions of orthogonally connected unit squares.
LINKS
A. Knopfmacher and M. E. Mays, Graph compositions I: Basic enumeration, Integers, 1 (2001), #A4.
J. N. Ridley and M. E. Mays, Compositions of unions of graphs, Fib. Quart., 42 (2004), 222-230.
Frank Simon, Algebraic Methods for Computing the Reliability of Networks, Dissertation, Doctor Rerum Naturalium (Dr. rer. nat.), Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden, 2012. - From N. J. A. Sloane, Jan 04 2013
EXAMPLE
For n=2 the a(2)=12 partitions of a 2x2 square are: 1 partition into a single 2x2 region; 4 partitions into a 3-square 'L' shape and an isolated corner; 2 partitions into 2 1x2 bricks; 4 partitions into a 1x2 brick and 2 isolated squares; and 1 partition into 4 isolated squares.
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Brian Kell, Oct 21 2008
EXTENSIONS
Terms for n=7,8,9 from Frank Simon, Oct 25 2011
a(10) from Frank Simon's thesis added by N. J. A. Sloane, Jan 04 2013
STATUS
approved