A068924 - OEIS

%I #17 Nov 28 2018 08:00:55

%S 6,3,2,2,4,4,6,8,10,14,18,24,32,42,56,74,98,130,172,228,302,400,530,

%T 702,930,1232,1632,2162,2864,3794,5026,6658,8820,11684,15478,20504,

%U 27162,35982,47666,63144,83648,110810,146792,194458,257602,341250

%N Number of ways to tile a 5 X 2n 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 4.

%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.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1).

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

%F 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]

%F a(n) = 2*A000931(n+3) for n>=3. - _R. J. Mathar_, Dec 06 2013

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

%K easy,nonn

%O 1,1

%A _Dean Hickerson_, Mar 11 2002