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A280362
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T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors and with new values introduced in order 0 sequentially upwards.
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5
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1, 2, 2, 4, 9, 4, 11, 50, 50, 11, 30, 285, 571, 285, 30, 82, 1617, 6727, 6727, 1617, 82, 224, 9188, 78800, 164326, 78800, 9188, 224, 612, 52193, 924579, 3992071, 3992071, 924579, 52193, 612, 1672, 296511, 10844773, 97147710, 201054068, 97147710
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OFFSET
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1,2
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COMMENTS
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Table starts
....1.......2...........4.............11...............30................82
....2.......9..........50............285.............1617..............9188
....4......50.........571...........6727............78800............924579
...11.....285........6727.........164326..........3992071..........97147710
...30....1617.......78800........3992071........201054068.......10144351660
...82....9188......924579.......97147710......10144351660.....1061399606602
..224...52193....10844773.....2363431872.....511688896140...111020011111453
..612..296511...127214104....57503068637...25812250379197.11613529410292966
.1672.1684466..1492251709..1399048151083.1302084964081326
.4568.9569425.17504551617.34038954765446
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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) +2*a(n-2) for n>4
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: [order 12]
k=4: [order 44]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..2..1. .0..0..1..2. .0..1..2..0. .0..1..2..0. .0..1..0..2
..0..2..1..0. .1..2..0..2. .0..2..1..2. .1..0..2..1. .0..2..1..2
..1..0..0..1. .2..1..2..1. .1..1..2..1. .0..2..0..1. .2..1..2..1
..0..2..2..1. .0..1..2..0. .0..0..1..0. .0..1..1..0. .2..0..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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