A192091 Number of tatami tilings of a 5 X n grid (with monomers allowed).

1, 8, 68, 90, 126, 178, 325, 584, 1165, 2030, 3619, 6080, 10987, 19362, 35477, 62360, 111837, 195614, 350707, 619568, 1112315, 1967090, 3514597, 6214984, 11093549, 19664558, 35090115, 62247552, 110934699, 196859394, 350650261

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 5 X 3 grid:
    _ _ _ _ _   _ _ _ _ _   _ _ _ _ _   _ _ _ _ _
   |_ _| |_| | |_| |_|_ _| | |_ _| |_| |_| | |_ _|
   |_ _|_| |_| | |_|_ _| | |_| |_|_| | | |_|_| | |
   |_|_ _|_|_| |_|_ _|_|_| |_|_|_ _|_| |_|_ _|_|_|

Crossrefs

Cf. A192090, A192092, A033508 (without tatami condition). Row sums of A272474.

Sequence in context: A000434 A304073 A250258 * A050841 A208947 A296670

Adjacent sequences: A192088 A192089 A192090 * A192092 A192093 A192094

Keyword

nonn

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 07 2011

Status

approved