A192097 Number of tatami tilings of an n X n square region with n monomers and floor(n * (n - 1) / 4) horizontal dimers.

1, 1, 2, 4, 8, 8, 16, 28, 40, 80, 144, 252, 456, 840

Offset: 0

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 15 2011

Keywords

• nonn
• more

Comments

A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.

There are at most n * (n - 1) / 2 horizontal dimers in any tiling of an n X n square with n monomers.

If there are floor(n * (n - 1) / 4) horizontal dimers, the numbers of horizontal dimers and vertical dimers differ by at most one.

Links

• 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.

Crossrefs

Cf. A192095.