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T(n,k)=Number of nXk 0..1 arrays with exactly floor(nXk/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order
12

%I #4 Feb 23 2013 17:09:23

%S 1,0,0,0,0,0,3,4,4,0,4,3,4,11,0,4,10,15,35,8,0,5,32,35,84,87,44,0,20,

%T 44,170,423,497,496,144,0,27,176,441,1753,2066,2862,1335,352,0,48,326,

%U 2192,8489,17674,23678,15420,7552,692,0,63,888,5416,39873,81537,195968,128889

%N T(n,k)=Number of nXk 0..1 arrays with exactly floor(nXk/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order

%C Table starts

%C .1.....0.......0........3..........4...........4............5...........20

%C .0.....0.......4........3.........10..........32...........44..........176

%C .0.....4.......4.......15.........35.........170..........441.........2192

%C .0....11......35.......84........423........1753.........8489........39873

%C .0.....8......87......497.......2066.......17674........81537.......800040

%C .0....44.....496.....2862......23678......195968......1802656.....17117005

%C .0...144....1335....15420.....128889.....2220730.....19892241....385142640

%C .0...352....7552....86570....1529195....25587208....473772613...8962277166

%C .0...692...21382...484976....8569032...297738400...5455705052.212898244002

%C .0..2488..122942..2751326..102004630..3488244716.132847734428

%C .0..6476..348597.15597305..577797690.41065342664

%C .0.17095.2045395.89022483.6918500106

%H R. H. Hardin, <a href="/A222509/b222509.txt">Table of n, a(n) for n = 1..145</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 2 is A222284

%Y Row 1 is A222283

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Feb 23 2013