A192090 Number of tatami tilings of a 4 X n grid (with monomers allowed).

1, 5, 29, 44, 66, 126, 238, 490, 922, 1714, 3306, 6246, 12102, 22994, 43682, 83810, 159154, 305062, 581382, 1108362, 2119602, 4037338, 7716554, 14720142, 28084702, 53639778, 102298794, 195341594, 372753634, 711338798, 1357975774

Offset: 0

Author

Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jun 23 2011

Keywords

• nonn
• easy

Comments

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

Examples

			Here are some tatami tilings of the 4 X 3 grid:
    _ _ _ _   _ _ _ _   _ _ _ _   _ _ _ _
   |_ _| |_| |_| |_ _| | |_ _| | |_| |_ _|
   |_ _|_| | | |_|_ _| |_| |_|_| | |_|_ _|
   |_|_ _|_| |_|_ _|_| |_|_|_ _| |_|_ _|_|
		

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.

Crossrefs

Cf. A180970, (3 X n grid), A192091 (5 X n grid), row sums of A272473.

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).