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An asymptotic estimate of the numbers of rectangular drawings or floorplans

A subdivision of a rectangle into rectangular faces with horizontal and vertical line segments is called rectangular drawings or floorplans. It is known that the number of rectangular drawings R(n) is asymptotically approximated by a geometric progression, where n is the number of inner rectangles. More precisely, there exists a constant c = lim<inf>n→∞</inf> R(n)<sup>1/n</sup>. The best upper and lower bounds of c ever known are 25 and 11.56, respectively. In this report, R(n) ≤ 13.5<sup>n−1</sup> is shown, which implies c ≤ 13.5.