A068924 Number of ways to tile a 5 X 2n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

6, 3, 2, 2, 4, 4, 6, 8, 10, 14, 18, 24, 32, 42, 56, 74, 98, 130, 172, 228, 302, 400, 530, 702, 930, 1232, 1632, 2162, 2864, 3794, 5026, 6658, 8820, 11684, 15478, 20504, 27162, 35982, 47666, 63144, 83648, 110810, 146792, 194458, 257602, 341250

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 4.
• F. Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages.
• Index entries for linear recurrences with constant coefficients, signature (0,1,1).

Crossrefs

Cf. A068930 for incongruent tilings, A068920 for more info. First column of A272474.

Formula

For n >= 6, a(n) = a(n-2) + a(n-3).

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

a(n) = 2*A000931(n+3) for n>=3. - R. J. Mathar, Dec 06 2013