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A295416
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.
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7
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1, 2, 2, 4, 10, 4, 7, 36, 36, 7, 12, 126, 234, 126, 12, 21, 454, 1534, 1534, 454, 21, 37, 1632, 10291, 19026, 10291, 1632, 37, 65, 5854, 68613, 240439, 240439, 68613, 5854, 65, 114, 21010, 457178, 3019079, 5741797, 3019079, 457178, 21010, 114, 200, 75412
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2........4..........7............12..............21.................37
...2....10.......36........126...........454............1632...............5854
...4....36......234.......1534.........10291...........68613.............457178
...7...126.....1534......19026........240439.........3019079...........37927609
..12...454....10291.....240439.......5741797.......136204120.........3232240913
..21..1632....68613....3019079.....136204120......6093564449.......272714953724
..37..5854...457178...37927609....3232240913....272714953724.....23025368248778
..65.21010..3048314..476686533...76727059034..12210363190599...1945003010538968
.114.75412.20323497.5990217198.1821136011730.546643613178667.164274708080518128
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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) -a(n-2) +a(n-3)
k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3)
k=3: a(n) = 6*a(n-1) +28*a(n-3) +3*a(n-4) +49*a(n-5) +33*a(n-6) -34*a(n-7) -22*a(n-8)
k=4: [order 14]
k=5: [order 37]
k=6: [order 78]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..0. .0..0..1..1
..1..0..1..1. .0..0..1..0. .0..1..1..1. .0..1..0..0. .1..1..1..1
..1..1..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1
..0..1..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1. .0..0..1..1
..0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..1..1..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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