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A302163
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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13
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1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 7, 10, 16, 13, 25, 12, 17, 21, 32, 21, 65, 20, 29, 31, 42, 64, 34, 185, 34, 51, 73, 57, 86, 128, 55, 385, 56, 109, 140, 156, 111, 179, 256, 89, 649, 94, 206, 296, 280, 361, 265, 370, 512, 144, 1489, 156, 407, 603, 635, 621, 865, 527, 770
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OFFSET
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1,2
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COMMENTS
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Table starts
...1...2...3....5....8...13....21....34....55.....89....144.....233.....377
...2...3...9...17...25...65...185...385...649...1489...3929....8609...15913
...4...6...7...12...20...34....56....94...156....262....436.....730....1216
...8..10..17...29...51..109...206...407...791...1584...3104....6165...12131
..16..21..31...73..140..296...603..1288..2584...5456..11189...23561...48423
..32..42..57..156..280..635..1247..2815..5524..12457..25230...55645..113410
..64..86.111..361..621.1563..2853..7306.12963..33522..61775..157788..293072
.128.179.265..865.1451.3948..6870.19993.32005.100147.163475..531350..820788
.256.370.527.1970.3189.9405.15489.50691.75825.282597.409385.1667452.2263018
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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) -2*a(n-4) +a(n-5)
k=3: a(n) = a(n-1) +8*a(n-3) -6*a(n-4) -4*a(n-6) +4*a(n-7) for n>11
k=4: [order 15] for n>19
k=5: [order 12] for n>15
k=6: [order 15] for n>26
k=7: [order 27] for n>39
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: a(n) = a(n-1) +a(n-2) -a(n-3) +2*a(n-4) for n>6
n=4: [order 22] for n>23
n=5: [order 36] for n>40
n=6: [order 35] for n>45
n=7: [order 80] 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..0..1. .0..1..0..1. .0..0..1..1. .0..1..1..0
..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..0..1..0. .0..1..1..0. .1..1..0..0
..0..1..0..1. .1..0..0..1. .1..0..1..0. .1..0..1..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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