%I #4 Jul 14 2012 11:32:31
%S 70,198,336,504,1320,1440,3696,3360,5040,8400,6720,10080,16632,16800,
%T 18480,20160,15120,33264,37800,30240,45360,73920,60480,65520,85680,
%U 55440,124740,142560,138600,151200,131040,180180,257040,110880,166320
%N Smallest size of which there are n tatamifree rooms.
%C A tatamifree room is a rectangle of even size that allows no 1x2 domino tiling satisfying the tatami rule, i.e. such that there is no point in which 4 tiles meet.
%C a(n)=A165632(A165765(n)) where A165765(n) is the least index for which A165633(A165765(n))=n.
%H Project Euler, <a href="http://projecteuler.net/index.php?section=problems&id=256">Problem 256: TatamiFree Rooms</a>, Sept. 2009.
%F A165764(n) = A165632(A165765(n)) = min { r*c in 2Z  #{{r,c}  A068920(r,c)=0 } = n }
%e The smallest tatamifree room is of size 7x10, and all other rectangles of this size allow for a tatami tiling, thus a(1) = 70.
%e a(5)=1320 is the smallest size of which there are exactly 5 tatamifree rooms, namely 20x66, 22x60, 24x55, 30x44 and 33x40.
%K nonn
%O 1,1
%A _M. F. Hasler_, Sep 26 2009
