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A192090 Number of tatami tilings of a 4 X n grid (with monomers allowed). 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jun 23 2011
STATUS
approved

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Last modified June 21 02:50 EDT 2024. Contains 373535 sequences. (Running on oeis4.)