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A192090
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Number of tatami tilings of a 4 X n grid (with monomers allowed).
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4
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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
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OFFSET
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0,2
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COMMENTS
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A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.
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LINKS
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FORMULA
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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).
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EXAMPLE
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Here are some tatami tilings of the 4 X 3 grid:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
|_ _| |_| |_| |_ _| | |_ _| | |_| |_ _|
|_ _|_| | | |_|_ _| |_| |_|_| | |_|_ _|
|_|_ _|_| |_|_ _|_| |_|_|_ _| |_|_ _|_|
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Frank Ruskey and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jun 23 2011
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STATUS
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approved
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