A068931 - OEIS

%I #13 Nov 28 2018 08:01:02

%S 1,6,2,2,1,1,1,1,1,1,2,2,2,2,2,3,3,4,4,4,4,5,6,7,7,8,8,10,12,13,14,15,

%T 17,20,21,26,26,31,34,38,44,47,56,60,66,78,82,100,104,122,134,148,176,

%U 186,217,238,266,310,328,393,417,483,543,594,694,745,870,960,1066,1237

%N Number of incongruent ways to tile a 6 X n room with 1x2 Tatami mats. At most 3 Tatami mats may meet at a point.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1311.6135">Paving rectangular regions with rectangular tiles,....</a>, arXiv:1311.6135 [math.CO], Table 13.

%H F. Ruskey and J. Woodcock, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r126">Counting Fixed-Height Tatami Tilings</a>, Electronic Journal of Combinatorics, Paper R126 (2009) 20 pages. [_Frank Ruskey_, Sep 26 2010]

%F For n >= 28, a(n) = a(n-5) + a(n-7) + a(n-10) + a(n-14) - a(n-15) - a(n-17) - a(n-19) - a(n-21).

%F G.f.: -x*(-1-6*x-2*x^2-3*x^16+6*x^15 +2*x^14-6*x^18 +2*x^7+7*x^8+2*x^9 +2*x^10 +6*x^11 +2*x^12+2*x^13-2*x^19-5*x^20-2*x^21 -6*x^22-2*x^23 +x^26 -2*x^3-x^4 +5*x^6)/ ((x^2-x+1) * (x^5+x^4+x^3-x-1) * (x^4-x^2+1) * (x^10 +x^8 +x^6-x^2-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by _R. J. Mathar_, Sep 16 2009

%Y Cf. A068925 for total number of tilings, A068926 for more info.

%K easy,nonn

%O 1,2

%A _Dean Hickerson_, Mar 11 2002