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A297637
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.
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13
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2, 3, 4, 5, 8, 8, 8, 29, 20, 16, 13, 69, 113, 51, 32, 21, 200, 374, 494, 132, 64, 34, 552, 1657, 2370, 2344, 341, 128, 55, 1641, 6548, 17305, 16508, 10587, 883, 256, 89, 4685, 28645, 108928, 201152, 109790, 48187, 2293, 512, 144, 13716, 119531, 771393
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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
...4....8......29.......69........200..........552...........1641
...8...20.....113......374.......1657.........6548..........28645
..16...51.....494.....2370......17305.......108928.........771393
..32..132....2344....16508.....201152......2077060.......25139952
..64..341...10587...109790....2171757.....36084211......715726580
.128..883...48187...740555...24145671....659362756....21730243952
.256.2293..222804..5099557..273842684..12330890209...681285029028
.512.5964.1027173.35164860.3092881435.229556423760.21128576143262
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LINKS
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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) = 4*a(n-1) -3*a(n-2) -4*a(n-4) -a(n-5) +a(n-6)
k=3: [order 15]
k=4: [order 32]
k=5: [order 68]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) +6*a(n-4) -28*a(n-5) -24*a(n-6)
n=3: [order 18]
n=4: [order 40]
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..1..0. .0..0..1..0. .1..0..0..1. .1..1..1..0. .1..1..0..0
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..1..0
..1..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..0. .1..1..0..0
..1..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..1..0. .1..1..0..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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