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Number of tatami tilings of a 7 X n grid (with monomers allowed).
2

%I #18 Jan 01 2023 09:47:18

%S 1,21,357,406,490,584,827,1090,1914,3262,6228,10226,17114,25534,41034,

%T 61778,102644,163334,278554,446898,747274,1175494,1926612,3021594,

%U 4960170,7880334,13028058,20841466,34355316,54835150,89785130

%N Number of tatami tilings of a 7 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 7 X 3 grid:

%e _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

%e |_ _| |_| |_| | |_| |_|_ _| |_| | |_ _| |_| |_| |_| | |_ _| |_|

%e |_ _|_| |_| |_| | |_|_ _| |_| | |_| |_|_| |_| | | |_|_| |_|_| |

%e |_|_ _|_|_|_|_| |_|_ _|_|_|_|_| |_|_|_ _|_|_|_| |_|_ _|_|_ _|_|

%Y Cf. A192092, A192094.

%K nonn

%O 0,2

%A _Frank Ruskey_ and Yuji Yamauchi (eugene.uti(AT)gmail.com), Jul 14 2011