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

0,2

Comments

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

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.

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).

Example

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

Crossrefs

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

Sequence in context: A117746 A156053 A081116 * A268673 A146829 A329151

Adjacent sequences: A192087 A192088 A192089 * A192091 A192092 A192093

Keyword

nonn,easy

Author

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

Status

approved