A068927 Number of incongruent ways to tile a 2 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

1, 1, 2, 3, 4, 6, 8, 12, 16, 24, 33, 49, 69, 102, 145, 214, 307, 452, 653, 960, 1393, 2046, 2978, 4371, 6376, 9354, 13665, 20041, 29307, 42972, 62884, 92191, 134974, 197858, 289772, 424746, 622198, 911970, 1336121, 1958319, 2869417, 4205538

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 9.
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,1,-1,0,-1).

Crossrefs

Cf. A068921 for total number of tilings, A068926 for more info.

Formula

For n >= 12, a(n) = a(n-1) + a(n-2) - a(n-5) + a(n-6) - a(n-7) - a(n-9).

G.f.: x*(1-x^10-2*x^8-2*x^6-x^4) / ((x^3+x-1) * (x^6+x^2-1)) [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.