%I #4 Jul 14 2012 11:32:31

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,2,1,1,

%T 1,3,1,1,1,2,1,1,1,1,1,2,1,1,1,1,2,2,2,2,2,1,1,1,1,1,2,1,1,1,1,1,1,4,

%U 2,1,1,1,1,3,1,1,1,1,2,2,2,1,1,1,1,2,2,2,1,1,1,1,1,2,1,2,1,1,1,2,4,2,1,1,1

%N Number of tatami-free rooms of given size A165632(n).

%C Number of rectangles of size A165632(n) which cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point.

%H Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;id=256">Problem 256: Tatami-Free Rooms</a>, Sept. 2009.

%F A165633 = #{ {r,c} | rc = A165632(n) }.

%e a(1)=1 because the rectangle of size 7x10 is the only one of size 70 that cannot be filled with 2x1 tiles without having 4 tiles meet in some point.

%e a(237)=5 because there are 5 different rectangles of size A165632(237)=1320 which cannot be tiled in the given way.

%Y Cf. A068920.

%K nonn

%O 1,14

%A _M. F. Hasler_, Sep 26 2009