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A283857
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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.
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13
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2, 4, 4, 8, 16, 8, 16, 61, 64, 16, 32, 233, 409, 256, 32, 64, 896, 2776, 2837, 1024, 64, 128, 3444, 19220, 35373, 19776, 4096, 128, 256, 13225, 131617, 456316, 448490, 137459, 16384, 256, 512, 50789, 901397, 5742620, 10741381, 5676420, 955680, 65536, 512
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OFFSET
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1,1
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COMMENTS
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Table starts
...2.....4.......8........16...........32.............64..............128
...4....16......61.......233..........896...........3444............13225
...8....64.....409......2776........19220.........131617...........901397
..16...256....2837.....35373.......456316........5742620.........72394838
..32..1024...19776....448490.....10741381......247708452.......5724272337
..64..4096..137459...5676420....252014450....10634931992.....449942735521
.128.16384..955680..71903903...5921518755...457711375590...35481195059121
.256.65536.6645662.910712188.139111379622.19691576356912.2796411775700471
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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)
k=3: [order 8]
k=4: [order 17]
k=5: [order 45]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4)
n=3: [order 14]
n=4: [order 28]
n=5: [order 74]
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..0..1. .0..0..1..0. .1..1..1..1. .0..0..0..0. .1..0..1..1
..0..1..1..0. .1..0..0..0. .0..1..0..0. .0..0..0..1. .1..0..1..1
..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..1
..1..1..0..0. .1..0..0..0. .1..0..0..1. .1..1..0..1. .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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