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A302150
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
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11
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1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 4, 1, 16, 1, 3, 5, 10, 1, 32, 1, 6, 11, 17, 28, 1, 64, 1, 10, 34, 56, 65, 84, 1, 128, 1, 21, 88, 255, 289, 257, 260, 1, 256, 1, 42, 271, 1038, 2005, 1529, 1025, 816, 1, 512, 1, 86, 798, 4771, 12212, 15999, 8152, 4097, 2576, 1, 1024, 1, 179
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OFFSET
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1,3
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COMMENTS
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Table starts
...1.1....1.....1......1.......1.........1..........1............1
...2.1....2.....2......3.......6........10.........21...........42
...4.1....4.....5.....11......34........88........271..........798
...8.1...10....17.....56.....255......1038.......4771........21866
..16.1...28....65....289....2005.....12212......83092.......578398
..32.1...84...257...1529...15999....145150....1482725.....15902462
..64.1..260..1025...8152..128319...1728734...26544210....439103633
.128.1..816..4097..43676.1030709..20614702..476725579..12181287002
.256.1.2576.16385.234707.8283143.245896061.8575073202.338788296901
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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) = a(n-1)
k=3: a(n) = 4*a(n-1) -2*a(n-2) -2*a(n-3)
k=4: a(n) = 5*a(n-1) -4*a(n-2) for n>3
k=5: [order 12]
k=6: [order 7] for n>9
k=7: [order 51] for n>54
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
n=3: [order 25] for n>27
n=4: [order 85] for n>89
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .0..1..1..1
..1..1..1..1. .1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..0
..0..1..1..0. .1..1..1..1. .0..1..1..0. .0..1..1..0. .1..1..1..0
..0..1..1..1. .0..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..1..1..0. .1..1..1..0. .1..1..1..0. .1..1..1..0. .0..1..1..0
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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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