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%I #4 Jul 14 2012 11:32:31
%S 70,88,96,108,126,130,140,150,154,160,176,180,192,198,204,208,216,228,
%T 234,238,240,250,252,260,266,270,280,286,294,300,304,308,320,322,330,
%U 336,340,348,352,360,368,372,374,378,384,390,396,400,408,414,416,418
%N Sizes of tatami-free rooms.
%C Even numbers s such that some rectangle of size s=r*c (r,c positive integers) cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point.
%C The number of different rectangles of size a(n) which have this property is given in A165633(n).
%H Project Euler, <a href="http://projecteuler.net/index.php?section=problems&id=256">Problem 256: Tatami-Free Rooms</a>
%F A165632 = { r*c in 2Z | A068920(r,c)=0 }
%e a(1)=70 because the rectangle of size 7x10 is the smallest that cannot be filled with 2x1 tiles without having 4 tiles meet in some point.
%Y Cf. A068920.
%K nonn
%O 1,1
%A _M. F. Hasler_, Sep 26 2009