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 A180970 Number of tatami tilings of a 3 X n grid (with monomers allowed). 3
 1, 3, 13, 22, 44, 90, 196, 406, 852, 1778, 3740, 7822, 16404, 34346, 72004, 150822, 316076, 662186, 1387596, 2907262, 6091780, 12763778, 26744268, 56036566, 117413804, 246015450, 515476036, 1080072022, 2263070868, 4741795442 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A tatami tiling consists of dimers (1 X 2) and monomers (1 X 1) where no four meet at a point. REFERENCES 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. LINKS A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, Monomer-Dimer Tatami Tilings of Rectangular Regions, Electronic Journal of Combinatorics, 18(1) (2011) P109. Alejandro Erickson, Frank Ruskey, Mark Schurch, Jennifer Woodcock, Auspicious tatami mat arrangements, arXiv:1103.3309 [math.CO], 2011. See p. 17. Index entries for linear recurrences with constant coefficients, signature (1,2,0,2,-1,-1). FORMULA 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). EXAMPLE 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: hh hh hh hh hh hh vv vm vm mm mv mv mm hh vv mv vm mm hh vv vv vm hh vv mv hh hh vv mv vm hh mm hh mv hh hh vm hh mm MATHEMATICA Join[{1, 3, 13}, LinearRecurrence[{1, 2, 0, 2, -1, -1}, {22, 44, 90, 196, 406, 852}, 27]] (* Jean-François Alcover, Jan 29 2019 *) CROSSREFS Cf. A180965 (2 X n grid), A192090 (4 X n grid), row sums of A272472. Sequence in context: A258774 A057589 A299645 * A135580 A166566 A011533 Adjacent sequences:  A180967 A180968 A180969 * A180971 A180972 A180973 KEYWORD nonn AUTHOR Frank Ruskey, Sep 29 2010 STATUS approved

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Last modified October 19 21:08 EDT 2019. Contains 328228 sequences. (Running on oeis4.)