A068923 Number of ways to tile a 4 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

1, 4, 4, 2, 3, 3, 3, 5, 5, 6, 8, 8, 11, 13, 14, 19, 21, 25, 32, 35, 44, 53, 60, 76, 88, 104, 129, 148, 180, 217, 252, 309, 365, 432, 526, 617, 741, 891, 1049, 1267, 1508, 1790, 2158, 2557, 3057, 3666, 4347, 5215, 6223, 7404, 8881, 10570, 12619, 15104, 17974

Offset: 1

Author

Dean Hickerson, Mar 11 2002

Keywords

• easy
• nonn

Links

• R. J. Mathar, Paving rectangular regions with rectangular tiles,...., arXiv:1311.6135 [math.CO], Table 3.
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1).

Crossrefs

Cf. A068929 for incongruent tilings, A068920 for more info. First column of A272473.

Formula

For n >= 9, a(n) = a(n-3) + a(n-5).

G.f.: x*(x+1)*(2*x^6+x^5+x^4-x^2-3*x-1)/(-1+x^5+x^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

Extensions

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