A200045 - OEIS

%I #31 Dec 09 2017 19:47:24

%S 4,16,252,64,3912,228984,256,59928,12870096,2545607472,1024,906912,

%T 696448224,465659203104,272454472598400,4096,13571712,36376835616,

%U 79102304162784,140221913588582784

%N Number T(n,m) of ways of 4-coloring an n X m grid so that there is no rectangle with all 4 corners the same color.

%C The rectangles have sides parallel to the x- and y-axes.

%H J. D. Davies, <a href="http://www.jasondavies.com/17x17/">Number of unique rectangle-free 4-colourings for an nxm grid</a>

%e Triangle starts:

%e      4;

%e     16,    252;

%e     64,   3912,    228984;

%e    256,  59928,  12870096,   2545607472;

%e   1024, 906912, 696448224, 465659203104, 272454472598400;

%e   ...

%Y Cf. A252778, A252780, A252839.

%K nonn,tabl,more

%O 1,1

%A _Jason Davies_, Nov 14 2011

%E T(6,5) from _Jason Davies_, Nov 08 2012