A192093 Number of tatami tilings of a 7 X n grid (with monomers allowed).

1, 21, 357, 406, 490, 584, 827, 1090, 1914, 3262, 6228, 10226, 17114, 25534, 41034, 61778, 102644, 163334, 278554, 446898, 747274, 1175494, 1926612, 3021594, 4960170, 7880334, 13028058, 20841466, 34355316, 54835150, 89785130

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

Table of n, a(n) for n=0..30.

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.

Example

Here are some tatami tilings of the 7 X 3 grid:
    _ _ _ _ _ _ _   _ _ _ _ _ _ _   _ _ _ _ _ _ _   _ _ _ _ _ _ _
   |_ _| |_| |_| | |_| |_|_ _| |_| | |_ _| |_| |_| |_| | |_ _| |_|
   |_ _|_| |_| |_| | |_|_ _| |_| | |_| |_|_| |_| | | |_|_| |_|_| |
   |_|_ _|_|_|_|_| |_|_ _|_|_|_|_| |_|_|_ _|_|_|_| |_|_ _|_|_ _|_|

Crossrefs

Cf. A192092, A192094.

Sequence in context: A300320 A271633 A184289 * A006105 A167032 A051564

Adjacent sequences: A192090 A192091 A192092 * A192094 A192095 A192096

Keyword

nonn

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 14 2011

Status

approved