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A269052
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T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.
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13
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3, 9, 9, 24, 42, 27, 60, 102, 174, 81, 144, 360, 594, 666, 243, 336, 1068, 3078, 3258, 2430, 729, 768, 3288, 13140, 24192, 17346, 8586, 2187, 1728, 9864, 58752, 149358, 183072, 90450, 29646, 6561, 3840, 29472, 253416, 971844, 1643376, 1350672, 464250
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OFFSET
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1,1
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COMMENTS
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Table starts
.....3.......9.......24.........60..........144............336.............768
.....9......42......102........360.........1068...........3288............9864
....27.....174......594.......3078........13140..........58752..........253416
....81.....666.....3258......24192.......149358.........971844.........6053094
...243....2430....17346.....183072......1643376.......15547380.......140497512
...729....8586....90450....1350672.....17696520......242861616......3193266318
..2187...29646...464250....9779808....187575858.....3726221592.....71430596250
..6561..100602..2353338...69793968...1964080920....56376679620...1577976495486
.19683..336798.11809746..492374976..20365312416...843461153880..34509932303172
.59049.1115370.58773858.3441051984.209472681102.12504078167988.748499855355192
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
k=5: [order 12] for n>13
k=6: [order 18] for n>19
k=7: [order 38] for n>39
Empirical for row n:
n=1: a(n) = 4*a(n-1) -4*a(n-2)
n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
n=4: [order 12] for n>14
n=5: [order 20] for n>22
n=6: [order 46] for n>48
n=7: [order 92] for n>94
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EXAMPLE
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Some solutions for n=4 k=4
..1..2..2..1. .1..2..1..0. .0..1..2..2. .0..1..0..1. .2..1..0..1
..2..2..2..1. .1..2..1..0. .2..1..2..1. .0..1..2..1. .2..1..2..1
..1..2..2..2. .1..0..1..2. .1..2..2..1. .2..1..0..1. .2..1..2..1
..1..2..1..2. .0..2..1..2. .1..2..2..2. .0..1..2..0. .2..1..2..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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