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A180970 Number of tatami tilings of a 3 by 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 (1x2) and monomers (1x1) 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

Table of n, a(n) for n=0..29.

A. Erickson, F. Ruskey, M. Schurch and J. Woodcock, Monomer-Dimer Tatami Tilings of Rectangular Regions, Electronic Journal of Combinatorics, 18(1) (2011) P109, and arXiv:1103.3309 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 2x3 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

CROSSREFS

Cf. A180965 (2 by n grid), A192090 (4 by n grid), row sums of A272472.

Sequence in context: A147105 A258774 A057589 * 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 August 23 11:46 EDT 2017. Contains 290995 sequences.