A068925 Number of ways to tile a 6 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

1, 9, 6, 3, 2, 2, 2, 1, 1, 2, 3, 4, 3, 3, 3, 4, 6, 6, 7, 6, 7, 9, 10, 13, 12, 14, 15, 17, 22, 22, 27, 27, 31, 37, 39, 49, 49, 58, 64, 70, 86, 88, 107, 113, 128, 150, 158, 193, 201, 235, 263, 286, 343, 359, 428, 464, 521, 606, 645, 771, 823, 949, 1070, 1166, 1377, 1468

Offset

1,2

Links

Table of n, a(n) for n=1..66.

R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 5.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,1).

Formula

For n >= 12, a(n) = a(n-5) + a(n-7).

G.f.: x*(1-2*x^10-6*x^9-11*x^8-6*x^7-7*x^6+x^5+2*x^4+3*x^3+6*x^2+9*x)/(1-x^7-x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by R. J. Mathar, Sep 16 2009

Crossrefs

Cf. A068931 for incongruent tilings, A068920 for more info.

Sequence in context: A093540 A252837 A198573 * A175616 A200232 A379394

Adjacent sequences: A068922 A068923 A068924 * A068926 A068927 A068928

Keyword

easy,nonn

Author

Dean Hickerson, Mar 11 2002

Status

approved