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A268628
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T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
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8
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3, 9, 9, 24, 42, 24, 60, 174, 174, 60, 144, 666, 1086, 666, 144, 336, 2430, 6300, 6300, 2430, 336, 768, 8586, 34890, 55452, 34890, 8586, 768, 1728, 29646, 187224, 467190, 467190, 187224, 29646, 1728, 3840, 100602, 982086, 3819654, 6000978, 3819654
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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
....9......42.......174.........666..........2430............8586
...24.....174......1086........6300.........34890..........187224
...60.....666......6300.......55452........467190.........3819654
..144....2430.....34890......467190.......6000978........74914554
..336....8586....187224.....3819654......74914554......1430057208
..768...29646....982086....30553014.....915847266.....26758514760
.1728..100602...5063964...240364746...11018667294....493042858032
.3840..336798..25764066..1866503592..130903914954...8974328440044
.8448.1115370.129678528.14342680944.1539375100362.161737670836314
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) -4*a(n-2)
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)
k=4: [order 6] for n>7
k=5: [order 10]
k=6: [order 14] for n>15
k=7: [order 26]
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EXAMPLE
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Some solutions for n=4 k=4
..2..1..0..0. .1..2..1..0. .0..0..0..0. .1..2..2..2. .0..0..0..1
..1..0..0..0. .0..1..0..0. .0..0..0..0. .2..1..2..2. .0..0..1..0
..2..0..1..0. .1..0..0..0. .1..0..0..0. .1..2..2..2. .0..0..0..1
..2..1..0..1. .0..0..1..1. .2..1..1..0. .0..2..2..2. .0..1..1..2
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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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