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T(n,k)=Number of nXk 0..1 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..1 order
7

%I #4 Feb 28 2013 17:28:12

%S 1,1,1,1,1,1,4,5,5,4,5,16,9,16,5,10,29,62,62,29,10,12,78,159,359,159,

%T 78,12,34,236,955,2002,2002,955,236,34,43,638,2609,12101,11878,12101,

%U 2609,638,43,101,1515,15700,73901,163123,163123,73901,15700,1515,101,127,4345

%N T(n,k)=Number of nXk 0..1 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..1 order

%C Table starts

%C ...1.....1.......1.........4............5.............10..............12

%C ...1.....1.......5........16...........29.............78.............236

%C ...1.....5.......9........62..........159............955............2609

%C ...4....16......62.......359.........2002..........12101...........73901

%C ...5....29.....159......2002........11878.........163123.........1025809

%C ..10....78.....955.....12101.......163123........2275891........32501123

%C ..12...236....2609.....73901......1025809.......32501123.......477839646

%C ..34...638...15700....460669.....14430600......470481133.....15677424850

%C ..43..1515...43653...2883822.....93266451.....6874602187....236833178725

%C .101..4345..265172..18178638...1330837238...101296942810...7904715597566

%C .127.11927..745702.115115070...8729138750..1501871230690.121438163564977

%C .331.32187.4553731.732065684.125508527702.22379588717639

%H R. H. Hardin, <a href="/A222703/b222703.txt">Table of n, a(n) for n = 1..161</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A222353

%Y Column 2 is A222535

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_ Feb 28 2013