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A297457
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0 or 2 neighboring 1s.
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13
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2, 3, 4, 5, 8, 8, 8, 25, 19, 16, 13, 57, 92, 48, 32, 21, 156, 285, 390, 120, 64, 34, 384, 1143, 1677, 1652, 299, 128, 55, 1009, 3933, 10579, 9774, 6888, 747, 256, 89, 2545, 14817, 52714, 97005, 55713, 28971, 1865, 512, 144, 6580, 52868, 303202, 693884, 862112
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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....8.....25.......57.......156.........384.........1009...........2545
...8...19.....92......285......1143........3933........14817..........52868
..16...48....390.....1677.....10579.......52714.......303202........1595942
..32..120...1652.....9774.....97005......693884......6088511.......46944276
..64..299...6888....55713....862112.....8800153....116817805.....1310421193
.128..747..28971...321030...7800563...113851142...2300975096....37653648610
.256.1865.121854..1848151..70510494..1469935404..45221328552..1078420953679
.512.4656.512165.10625522.636242985.18934230754.886373249313.30786030956559
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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) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4)
k=3: a(n) = 5*a(n-1) -3*a(n-2) +4*a(n-3) -25*a(n-4) +10*a(n-5) -7*a(n-6) +12*a(n-7)
k=4: [order 11]
k=5: [order 27]
k=6: [order 55]
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) +a(n-3) +4*a(n-4)
n=3: a(n) = 3*a(n-1) +4*a(n-2) -7*a(n-3) +8*a(n-4) -19*a(n-5) +8*a(n-6) +2*a(n-8)
n=4: [order 15]
n=5: [order 33]
n=6: [order 72]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..0
..0..0..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..0. .1..0..0..1
..0..0..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0
..0..0..0..1. .0..0..0..1. .0..0..1..1. .1..0..0..0. .0..0..1..0
..0..0..0..0. .0..1..0..0. .0..1..1..0. .0..0..0..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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