%I #8 Jun 24 2014 01:08:23
%S 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,
%T 93,114,130,161,188,223,268,318,378,456,533,646,763,911,1092,1296,
%U 1542,1855,2190,2634,3133,3732,4463,5323,6339,7596,9022,10802,12876
%N 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.
%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.
%F 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).
%F 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]
%Y Cf. A068923 for total number of tilings, A068926 for more info.
%K easy,nonn
%O 1,2
%A _Dean Hickerson_, Mar 11 2002
%E G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.