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

Author

Dean Hickerson, Mar 11 2002

Keywords

• easy
• nonn

Comments

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

Links

• R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 5.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,1).

Crossrefs

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

Formula

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) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

Extensions

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.