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%I #26 Jan 01 2023 09:47:29
%S 1,5,29,44,66,126,238,490,922,1714,3306,6246,12102,22994,43682,83810,
%T 159154,305062,581382,1108362,2119602,4037338,7716554,14720142,
%U 28084702,53639778,102298794,195341594,372753634,711338798,1357975774
%N Number of tatami tilings of a 4 X n grid (with monomers allowed).
%C A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point.
%H Alois P. Heinz, <a href="/A192090/b192090.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, <a href="https://doi.org/10.37236/596">Monomer-Dimer Tatami Tilings of Rectangular Regions</a>, Electronic Journal of Combinatorics, 18(1) (2011) P109, 24 pages.
%F 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).
%e Here are some tatami tilings of the 4 X 3 grid:
%e _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e |_ _| |_| |_| |_ _| | |_ _| | |_| |_ _|
%e |_ _|_| | | |_|_ _| |_| |_|_| | |_|_ _|
%e |_|_ _|_| |_|_ _|_| |_|_|_ _| |_|_ _|_|
%Y Cf. A180970, (3 X n grid), A192091 (5 X n grid), row sums of A272473.
%K nonn,easy
%O 0,2
%A _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jun 23 2011
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