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A180970 Number of tatami tilings of a 3 X n grid (with monomers allowed). 3

%I

%S 1,3,13,22,44,90,196,406,852,1778,3740,7822,16404,34346,72004,150822,

%T 316076,662186,1387596,2907262,6091780,12763778,26744268,56036566,

%U 117413804,246015450,515476036,1080072022,2263070868,4741795442

%N Number of tatami tilings of a 3 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.

%D A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, Auspicious Tatami Mat Arrangements, The 16th Annual International Computing and Combinatorics Conference (COCOON 2010), July 19-21, Nha Trang, Vietnam. LNCS 6196 (2010) 288-297.

%H A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, <a href="http://www.combinatorics.org/Volume_18/Abstracts/v18i1p109.html">Monomer-Dimer Tatami Tilings of Rectangular Regions</a>, Electronic Journal of Combinatorics, 18(1) (2011) P109.

%H Alejandro Erickson, Frank Ruskey, Mark Schurch, Jennifer Woodcock, <a href="https://arxiv.org/abs/1103.3309">Auspicious tatami mat arrangements</a>, arXiv:1103.3309 [math.CO], 2011. See p. 17.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,2,-1,-1).

%F G.f.: (1 + 2z + 8z^2 + 3z^3 - 6z^4 - 3z^5 - 4z^6 + 2z^7 + z^8)/(1 - z - 2z^2 - 2z^4 + z^5 + z^6).

%e Below we show the a(2) = 13 tatami tilings of a 2 X 3 rectangle where v = square of a vertical dimer, h = square of a horizontal dimer, m = monomer:

%e hh hh hh hh hh hh vv vm vm mm mv mv mm

%e hh vv mv vm mm hh vv vv vm hh vv mv hh

%e hh vv mv vm hh mm hh mv hh hh vm hh mm

%t Join[{1, 3, 13}, LinearRecurrence[{1, 2, 0, 2, -1, -1}, {22, 44, 90, 196, 406, 852}, 27]] (* _Jean-Fran├žois Alcover_, Jan 29 2019 *)

%Y Cf. A180965 (2 X n grid), A192090 (4 X n grid), row sums of A272472.

%K nonn

%O 0,2

%A _Frank Ruskey_, Sep 29 2010

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)