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%I #4 Nov 30 2014 19:48:04
%S 40,180,180,816,1246,816,3728,8870,8870,3728,17152,65040,102811,65040,
%T 17152,79424,489772,1273440,1273440,489772,79424,369920,3775022,
%U 16687766,27920380,16687766,3775022,369920,1731840,29664576,228610911,667858580
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to a nonzero multiple of 2
%C Table starts
%C .......40.........180............816.............3728...............17152
%C ......180........1246...........8870............65040..............489772
%C ......816........8870.........102811..........1273440............16687766
%C .....3728.......65040........1273440.........27920380...........667858580
%C ....17152......489772.......16687766........667858580.........29868134632
%C ....79424.....3775022......228610911......16965787428.......1430667235078
%C ...369920....29664576.....3233921644.....447556857260......71260903869938
%C ..1731840...236740252....46763019686...12076357468990....3627694408668076
%C ..8144896..1912108322...686058347195..330184315214356..186917463235694336
%C .38458368.15584536740.10159339091240.9097022461368016.9695744269718563214
%H R. H. Hardin, <a href="/A251210/b251210.txt">Table of n, a(n) for n = 1..264</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) -12*a(n-2) -16*a(n-3)
%F k=2: a(n) = 18*a(n-1) -90*a(n-2) +7*a(n-3) +576*a(n-4) +210*a(n-5) -180*a(n-6)
%F k=3: [order 14]
%F k=4: [order 30]
%F k=5: [order 65]
%e Some solutions for n=3 k=4
%e ..0..0..0..0..0....0..0..0..2..2....0..0..1..2..2....0..0..0..0..0
%e ..2..0..2..0..2....2..0..2..2..0....0..2..1..0..0....0..2..2..0..2
%e ..0..0..2..2..2....2..2..2..2..0....2..0..1..0..2....0..2..0..0..2
%e ..0..2..2..0..2....1..1..1..1..1....1..1..0..1..1....2..2..2..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014
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