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%I #23 Jan 01 2023 09:47:25
%S 1,8,68,90,126,178,325,584,1165,2030,3619,6080,10987,19362,35477,
%T 62360,111837,195614,350707,619568,1112315,1967090,3514597,6214984,
%U 11093549,19664558,35090115,62247552,110934699,196859394,350650261
%N Number of tatami tilings of a 5 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 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.
%e Here are some tatami tilings of the 5 X 3 grid:
%e _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e |_ _| |_| | |_| |_|_ _| | |_ _| |_| |_| | |_ _|
%e |_ _|_| |_| | |_|_ _| | |_| |_|_| | | |_|_| | |
%e |_|_ _|_|_| |_|_ _|_|_| |_|_|_ _|_| |_|_ _|_|_|
%Y Cf. A192090, A192092, A033508 (without tatami condition). Row sums of A272474.
%K nonn
%O 0,2
%A _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 07 2011
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