A068931 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.

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

Offset

1,2

Links

Table of n, a(n) for n=1..70.

R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 13.

F. Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages. [Frank Ruskey, Sep 26 2010]

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)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by R. J. Mathar, Sep 16 2009

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

Keyword

easy,nonn

Author

Dean Hickerson, Mar 11 2002

Status

approved