OFFSET
0,2
COMMENTS
A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, Monomer-Dimer Tatami Tilings of Rectangular Regions, Electronic Journal of Combinatorics, 18(1) (2011) P109, 24 pages.
FORMULA
G.f.: -13 + 3*x + 3*x^2 + 2*x^3 + (14 - 12*x + 10*x^2 + 10*x^4 - 104*x^5 + 114*x^6 - 80*x^7 + 34*x^8 + 12*x^9 - 2*x^10)/(1 - x - x^2 - x^3 + x^4 - 7*x^5 + 7*x^6 - x^7 + x^8 + x^9 + x^10 - x^11).
EXAMPLE
Here are some tatami tilings of the 4 X 3 grid:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
|_ _| |_| |_| |_ _| | |_ _| | |_| |_ _|
|_ _|_| | | |_|_ _| |_| |_|_| | |_|_ _|
|_|_ _|_| |_|_ _|_| |_|_|_ _| |_|_ _|_|
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jun 23 2011
STATUS
approved