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A240484
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T(n,k)=Number of nXk 0..1 arrays with no element equal to more than two horizontal or vertical neighbors, with new values 0..1 introduced in row major order
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8
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1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 81, 122, 81, 16, 32, 264, 578, 578, 264, 32, 64, 857, 2753, 4104, 2753, 857, 64, 128, 2785, 13147, 29084, 29084, 13147, 2785, 128, 256, 9050, 62781, 205754, 306749, 205754, 62781, 9050, 256, 512, 29407, 299758, 1455916
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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.........8..........16............32..............64
...2.....8......25........81.........264...........857............2785
...4....25.....122.......578........2753.........13147...........62781
...8....81.....578......4104.......29084........205754.........1455916
..16...264....2753.....29084......306749.......3229199........33986995
..32...857...13147....205754.....3229199......50525365.......790390105
..64..2785...62781...1455916....33986995.....790390105.....18384693920
.128..9050..299758..10304849...357678069...12362251350....427494590110
.256.29407.1431221..72937769..3764378216..193349390970...9939634161916
.512.95557.6833530.516249590.39618451066.3024029579084.231101074704277
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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) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 4*a(n-1) +3*a(n-2) +2*a(n-3) +6*a(n-4) +2*a(n-5) -a(n-6)
k=4: [order 22]
k=5: [order 54]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....0..1..1..0....0..0..1..1....0..1..0..1....0..0..0..1
..1..1..1..0....0..0..1..0....1..0..1..0....0..1..0..0....0..1..1..0
..0..0..1..0....1..0..1..0....0..1..0..0....1..0..1..0....0..1..0..1
..0..1..0..1....1..0..1..0....0..0..1..1....1..0..0..0....0..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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