%I #4 Feb 17 2013 17:09:22

%S 1,1,1,1,1,1,4,5,5,4,5,18,9,18,5,14,63,118,118,63,14,17,234,498,1391,

%T 498,234,17,75,1163,8111,20340,20340,8111,1163,75,95,4953,37107,

%U 342953,271141,342953,37107,4953,95,411,24021,676485,6221698,16985929,16985929

%N T(n,k)=Number of nXk 0..3 arrays with no more than floor(nXk/2) elements unequal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..3 order

%C Table starts

%C ....1......1........1..........4...........5..........14..........17

%C ....1......1........5.........18..........63.........234........1163

%C ....1......5........9........118.........498........8111.......37107

%C ....4.....18......118.......1391.......20340......342953.....6221698

%C ....5.....63......498......20340......271141....16985929...286125939

%C ...14....234.....8111.....342953....16985929...963154789.61522684225

%C ...17...1163....37107....6221698...286125939.61522684225

%C ...75...4953...676485..113556454.20743320247

%C ...95..24021..3140167.2103238076

%C ..411.109395.58995438

%C ..519.536457

%C .2522

%H R. H. Hardin, <a href="/A222378/b222378.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=4 k=4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..1..1..1....0..1..2..2

%e ..0..0..0..0....0..0..0..0....1..1..0..0....0..2..1..1....1..1..1..2

%e ..0..0..1..0....0..0..0..0....2..0..0..0....3..1..1..1....1..1..1..1

%e ..2..1..0..0....1..0..2..2....0..0..0..0....1..1..1..1....1..1..1..1

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Feb 17 2013