%I #9 Oct 17 2019 11:40:58
%S 2,2,2,4,5,9,12,21,30,51,76,127,195,322,504,826,1309,2135,3410,5545,
%T 8900,14445,23256,37701,60813,98514,159094,257608,416325,673933,
%U 1089648,1763581,2852242,4615823,7466468,12082291,19546175,31628466
%N Number of incongruent ways to tile a 3 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 10.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,0,-1,-1).
%F For n >= 8, a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-5) - a(n-6).
%F O.g.f.: x(2-4x^2-x^4+x^6)/((1-x-x^2)(1-x^2-x^4)). a(n) = (A000045(n+1)+A053602(n+1))/2, n>1. [From _R. J. Mathar_, Aug 30 2008]
%Y Cf. A068922 for total number of tilings, A068926 for more info.
%Y Essentially the same as A001224.
%K easy,nonn
%O 1,1
%A _Dean Hickerson_, Mar 11 2002