A068927 - OEIS

A068927

Number of incongruent ways to tile a 2 X n room with 1 X 2 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..42.

R. J. Mathar, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 9.

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

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)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by R. J. Mathar, Sep 16 2009

CROSSREFS

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

Sequence in context: A018425 A018328 A018280 * A336613 A018261 A306201

Adjacent sequences: A068924 A068925 A068926 * A068928 A068929 A068930

KEYWORD

easy,nonn

AUTHOR

Dean Hickerson, Mar 11 2002

STATUS

approved