%I #5 Mar 31 2012 12:35:50
%S 1,1,1,1,3,1,2,6,6,2,3,18,25,18,3,6,60,164,164,60,6,10,210,1092,2101,
%T 1092,210,10,20,756,7954,29100,29100,7954,756,20,35,2772,57519,417190,
%U 807261,417190,57519,2772,35,70,10296,429936,6104168,23226996,23226996
%N T(n,k)=Half the number of nXk binary arrays with the number of 1-1 adjacencies equal to the number of 0-0 adjacencies
%C Table starts
%C ..1.....1........1...........2..............3.................6
%C ..1.....3........6..........18.............60...............210
%C ..1.....6.......25.........164...........1092..............7954
%C ..2....18......164........2101..........29100............417190
%C ..3....60.....1092.......29100.........807261..........23226996
%C ..6...210.....7954......417190.......23226996........1333831052
%C .10...756....57519.....6104168......679637064.......78105333988
%C .20..2772...429936....90554742....20179029954.....4635786110412
%C .35.10296..3205504..1356933444...604725622404...277890240523800
%C .70.38610.24288784.20489622108.18266061977928.16785123061670988
%H R. H. Hardin, <a href="/A183253/b183253.txt">Table of n, a(n) for n = 1..3000</a>
%e Some solutions with a(1,1)=0 for 4X6
%e ..0..0..0..0..0..1....0..0..0..0..1..1....0..0..0..0..1..0....0..0..0..1..0..1
%e ..1..1..1..0..1..0....1..1..0..1..1..1....0..0..0..1..1..1....0..0..1..1..1..1
%e ..0..1..1..1..1..1....1..1..0..0..0..0....1..0..1..0..0..1....0..1..1..0..1..1
%e ..0..0..0..0..0..1....1..1..0..0..1..0....1..1..1..1..1..0....0..1..0..0..0..0
%Y Column 1 is A001405(n-2)
%Y Column 2 is 3*A000984(n-2)
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 03 2011