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A268766
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T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
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7
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0, 1, 1, 2, 6, 2, 5, 15, 15, 5, 10, 44, 56, 44, 10, 20, 105, 223, 223, 105, 20, 38, 258, 762, 1148, 762, 258, 38, 71, 595, 2607, 5170, 5170, 2607, 595, 71, 130, 1368, 8500, 23156, 32056, 23156, 8500, 1368, 130, 235, 3069, 27411, 99057, 193573, 193573, 99057
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OFFSET
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1,4
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COMMENTS
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Table starts
...0....1......2.......5........10.........20...........38............71
...1....6.....15......44.......105........258..........595..........1368
...2...15.....56.....223.......762.......2607.........8500.........27411
...5...44....223....1148......5170......23156........99057........418924
..10..105....762....5170.....32056.....193573......1129042.......6475898
..20..258...2607...23156....193573....1552272.....12111209......92571436
..38..595...8500...99057...1129042...12111209....127676872....1312123185
..71.1368..27411..418924...6475898...92571436...1312123185...18045771274
.130.3069..86622.1736105..36505596..696659613..13311824510..245588158242
.235.6830.270955.7122856.203462597.5178525870.133228716170.3292985469950
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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) +a(n-2) -2*a(n-3) -a(n-4)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4)
k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6)
k=4: [order 8]
k=5: [order 12]
k=6: [order 16]
k=7: [order 28]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .1..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..1..0
..0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..1. .0..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1
..0..1..0..0. .0..1..0..0. .0..1..0..0. .1..0..0..1. .0..1..0..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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