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A165764 Smallest size of which there are n tatami-free rooms.

%I A165764 #4 Jul 14 2012 11:32:31
%S A165764 70,198,336,504,1320,1440,3696,3360,5040,8400,6720,10080,16632,16800,
%T A165764 18480,20160,15120,33264,37800,30240,45360,73920,60480,65520,85680,
%U A165764 55440,124740,142560,138600,151200,131040,180180,257040,110880,166320
%N A165764 Smallest size of which there are n tatami-free rooms.
%C A165764 A tatami-free 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 A165764 a(n)=A165632(A165765(n)) where A165765(n) is the least index for which A165633(A165765(n))=n.
%H A165764 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;id=256">Problem 256: Tatami-Free Rooms</a>, Sept. 2009.
%F A165764 A165764(n) = A165632(A165765(n)) = min { r*c in 2Z | #{{r,c} | A068920(r,c)=0 } = n }
%e A165764 The smallest tatami-free room is of size 7x10, and all other rectangles of this size allow for a tatami tiling, thus a(1) = 70.
%e A165764 a(5)=1320 is the smallest size of which there are exactly 5 tatami-free rooms, namely 20x66, 22x60, 24x55, 30x44 and 33x40.
%K A165764 nonn
%O A165764 1,1
%A A165764 _M. F. Hasler_, Sep 26 2009