A068929 Number of incongruent ways to tile a 4 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

1, 3, 2, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 8, 8, 11, 12, 14, 17, 20, 24, 29, 32, 41, 46, 56, 68, 78, 93, 114, 130, 161, 188, 223, 268, 318, 378, 456, 533, 646, 763, 911, 1092, 1296, 1542, 1855, 2190, 2634, 3133, 3732, 4463, 5323, 6339, 7596, 9022, 10802, 12876

Offset

1,2

Links

Table of n, a(n) for n=1..57.

F. Ruskey and J. Woodcock, Counting Fixed-Height Tatami Tilings, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages.

Formula

For n >= 20, a(n) = a(n-3) + a(n-5) + a(n-6) - a(n-9) + a(n-10) - a(n-11) - a(n-13) - a(n-15).

G.f.: x*(1-x^18+x^17+x^16+x^15+x^13-x^12-2*x^11-2*x^8-4*x^7-3*x^6-x^5-x^4+2*x^2+3*x) / ((x^5+x^3-1) * (x^10+x^6-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

Crossrefs

Cf. A068923 for total number of tilings, A068926 for more info.

Sequence in context: A213195 A256794 A366899 * A060567 A174543 A260450

Adjacent sequences: A068926 A068927 A068928 * A068930 A068931 A068932

Keyword

easy,nonn

Author

Dean Hickerson, Mar 11 2002

Extensions

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

Status

approved