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A228683
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T(n,k)=Number of nXk binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
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12
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2, 3, 4, 5, 7, 8, 8, 19, 17, 16, 13, 40, 77, 41, 32, 21, 97, 216, 313, 99, 64, 34, 217, 809, 1152, 1277, 239, 128, 55, 508, 2529, 6737, 6160, 5215, 577, 256, 89, 1159, 8832, 28977, 56549, 32928, 21305, 1393, 512, 144, 2683, 28793, 152048, 333517, 475809, 176032
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OFFSET
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1,1
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COMMENTS
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Table starts
...2....3......5.......8........13.........21...........34............55
...4....7.....19......40........97........217..........508..........1159
...8...17.....77.....216.......809.......2529.........8832.........28793
..16...41....313....1152......6737......28977.......152048........699833
..32...99...1277....6160.....56549.....333517......2644336......17124415
..64..239...5215...32928....475809....3837761.....46125216.....419022831
.128..577..21305..176032...4008817...44171841....806190208...10258304689
.256.1393..87049..941056..33795201..508425617..14105294112..251170142257
.512.3363.355685.5030848.284980061.5852202757.246929287360.6150224353031
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..1057
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2) -3*a(n-3)
k=4: a(n) = 6*a(n-1) -2*a(n-2) -8*a(n-3)
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)
k=6: [order 7]
k=7: [order 12]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2)
n=3: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)
n=4: a(n) = 2*a(n-1) +16*a(n-2) -7*a(n-3) -18*a(n-4)
n=5: [order 7]
n=6: [order 10]
n=7: [order 16]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0
..0..1..0..1....1..0..0..0....0..0..1..0....0..0..1..0....1..0..0..0
..0..0..0..0....0..0..0..1....1..0..1..0....0..0..1..0....1..0..0..0
..0..0..0..1....0..1..0..1....1..0..0..0....0..0..1..0....0..0..0..0
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CROSSREFS
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Column 1 is A000079
Column 2 is A001333(n+1)
Diagonal is A067963
Row 1 is A000045(n+2)
Row 2 is A006130(n+1)
Sequence in context: A112922 A305077 A302175 * A133017 A290019 A161924
Adjacent sequences: A228680 A228681 A228682 * A228684 A228685 A228686
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KEYWORD
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nonn,tabl,look
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AUTHOR
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R. H. Hardin Aug 30 2013
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STATUS
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approved
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