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%I #17 Oct 26 2018 09:40:06
%S 1,1,1,1,2,1,1,4,4,1,1,8,14,8,1,1,16,50,50,16,1,1,32,178,276,178,32,1,
%T 1,64,634,1498,1498,634,64,1,1,128,2258,8352,10980,8352,2258,128,1,1,
%U 256,8042,46730,85138,85138,46730,8042,256,1,1,512,28642,260204,655090,781712,655090,260204,28642,512,1
%N Number A(n,k) of 2-colorings of a k X n rectangle such that no nontrivial subsquare has monochromatic corners; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%H Alois P. Heinz, <a href="/A255256/b255256.txt">Antidiagonals n = 0..12</a>
%e A(2,2) = 2^(2*2) - 2 = 14 because there are exactly two of sixteen 2-colorings of the 2 X 2 square resulting in nontrivial subsquares with monochromatic corners.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 4, 8, 16, 32, 64, ...
%e 1, 4, 14, 50, 178, 634, 2258, ...
%e 1, 8, 50, 276, 1498, 8352, 46730, ...
%e 1, 16, 178, 1498, 10980, 85138, 655090, ...
%e 1, 32, 634, 8352, 85138, 781712, 6965108, ...
%e 1, 64, 2258, 46730, 655090, 6965108, 58339148, ...
%Y Columns (or rows) k=0-5 give: A000012, A000079, A055099, A133357, A255255, A255262.
%Y Main diagonal gives A018803.
%K nonn,tabl
%O 0,5
%A _Alois P. Heinz_, Feb 19 2015