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%I #9 Sep 10 2016 06:04:24
%S 2,3,4,5,7,8,8,19,17,16,13,40,77,41,32,21,97,216,313,99,64,34,217,809,
%T 1152,1277,239,128,55,508,2529,6737,6160,5215,577,256,89,1159,8832,
%U 28977,56549,32928,21305,1393,512,144,2683,28793,152048,333517,475809,176032
%N T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
%C Table starts
%C ...2....3......5.......8........13.........21...........34............55
%C ...4....7.....19......40........97........217..........508..........1159
%C ...8...17.....77.....216.......809.......2529.........8832.........28793
%C ..16...41....313....1152......6737......28977.......152048........699833
%C ..32...99...1277....6160.....56549.....333517......2644336......17124415
%C ..64..239...5215...32928....475809....3837761.....46125216.....419022831
%C .128..577..21305..176032...4008817...44171841....806190208...10258304689
%C .256.1393..87049..941056..33795201..508425617..14105294112..251170142257
%C .512.3363.355685.5030848.284980061.5852202757.246929287360.6150224353031
%H R. H. Hardin, <a href="/A228683/b228683.txt">Table of n, a(n) for n = 1..1057</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2)
%F k=3: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3)
%F k=4: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3)
%F k=5: a(n) = 12*a(n-1) -27*a(n-2) -32*a(n-3) +49*a(n-4) +20*a(n-5) -5*a(n-6)
%F k=6: [order 7]
%F k=7: [order 12]
%F Empirical for row n:
%F n=1: a(n) = a(n-1) +a(n-2)
%F n=2: a(n) = a(n-1) +3*a(n-2)
%F n=3: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)
%F n=4: a(n) = 2*a(n-1) +16*a(n-2) -7*a(n-3) -18*a(n-4)
%F n=5: [order 7]
%F n=6: [order 10]
%F n=7: [order 16]
%e Some solutions for n=4 k=4
%e ..0..0..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0
%e ..0..1..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0
%e ..0..0..0..0....0..0..0..1....1..0..1..0....0..0..1..0....1..0..0..0
%e ..0..0..0..1....0..1..0..1....1..0..0..0....0..0..1..0....0..0..0..0
%Y Column 1 is A000079
%Y Column 2 is A001333(n+1)
%Y Diagonal is A067963
%Y Row 1 is A000045(n+2)
%Y Row 2 is A006130(n+1)
%K nonn,tabl,look
%O 1,1
%A _R. H. Hardin_ Aug 30 2013
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