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A068931
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Number of incongruent ways to tile a 6 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.
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2
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1, 6, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 6, 7, 7, 8, 8, 10, 12, 13, 14, 15, 17, 20, 21, 26, 26, 31, 34, 38, 44, 47, 56, 60, 66, 78, 82, 100, 104, 122, 134, 148, 176, 186, 217, 238, 266, 310, 328, 393, 417, 483, 543, 594, 694, 745, 870, 960, 1066, 1237
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| F. Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages. [From Frank Ruskey (ruskey(AT)cs.uvic.ca), Sep 26 2010]
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FORMULA
| For n >= 28, a(n) = a(n-5) + a(n-7) + a(n-10) + a(n-14) - a(n-15) - a(n-17) - a(n-19) - a(n-21).
G.f.: -x*(-1-6*x-2*x^2-3*x^16+6*x^15+2*x^14-6*x^18+2*x^7+7*x^8+2*x^9+2*x^10+6*x^11+2*x^12+2*x^13-2*x^19-5*x^20-2*x^21-6*x^22-2*x^23+x^26-2*x^3-x^4+5*x^6)/ ((x^2-x+1) * (x^5+x^4+x^3-x-1) * (x^4-x^2+1) * (x^10+x^8+x^6-x^2-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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CROSSREFS
| Cf. A068925 for total number of tilings, A068926 for more info.
Sequence in context: A110321 A111553 A141473 * A061666 A136708 A020795
Adjacent sequences: A068928 A068929 A068930 * A068932 A068933 A068934
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KEYWORD
| easy,nonn
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 11 2002
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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