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 A165764 Smallest size of which there are n tatami-free rooms. 2

%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 tatami-free rooms.

%C 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 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&amp;id=256">Problem 256: Tatami-Free 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 tatami-free 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 tatami-free rooms, namely 20x66, 22x60, 24x55, 30x44 and 33x40.

%K nonn

%O 1,1

%A _M. F. Hasler_, Sep 26 2009

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Last modified September 11 01:27 EDT 2024. Contains 375813 sequences. (Running on oeis4.)