A192097 - OEIS

%I #18 Dec 16 2016 03:05:48

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

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

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

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

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

%H A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, <a href="http://www.combinatorics.org/Volume_18/Abstracts/v18i1p109.html">Monomer-Dimer Tatami Tilings of Rectangular Regions</a>, Electronic Journal of Combinatorics, 18(1) (2011) P109, 24 pages.

%Y Cf. A192095.

%K nonn,more

%O 0,3

%A _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 15 2011