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A228683 T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.

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