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A280859
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T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
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8
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1, 2, 2, 4, 9, 4, 11, 29, 29, 11, 30, 110, 46, 110, 30, 82, 442, 96, 96, 442, 82, 224, 1708, 256, 124, 256, 1708, 224, 612, 6596, 678, 216, 216, 678, 6596, 612, 1672, 25624, 1698, 462, 282, 462, 1698, 25624, 1672, 4568, 99432, 4358, 1005, 491, 491, 1005, 4358
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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..224...612..1672...4568...12480...34096
....2......9....29..110..442.1708.6596.25624.99432.385584.1495696.5802080
....4.....29....46...96..256..678.1698..4358.11218..28650...73354..188066
...11....110....96..124..216..462.1005..2010..3907...7756...15749...31804
...30....442...256..216..282..491..968..1857..3220...5281....8574...14339
...82...1708...678..462..491..712.1202..2268..4220...7108...11240...17330
..224...6596..1698.1005..968.1202.1738..2877..5244...9569...15872...24653
..612..25624..4358.2010.1857.2268.2877..4124..6722..12044...21713...35572
.1672..99432.11218.3907.3220.4220.5244..6722..9562..15351...27000...48087
.4568.385584.28650.7756.5281.7108.9569.12044.15351..21752...34547...59836
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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) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
k=3: a(n) = 2*a(n-1) +4*a(n-3) -a(n-4) +2*a(n-6) -2*a(n-7) for n>9
k=4: [order 12] for n>16
k=5: [order 12] for n>18
k=6: [order 16] for n>22
k=7: [order 23] for n>29
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..2. .0..1..0..0. .0..1..2..2. .0..0..1..1. .0..0..1..0
..2..2..0..2. .0..2..2..1. .0..1..0..1. .1..2..2..0. .1..2..1..2
..0..1..0..1. .1..1..0..1. .2..2..0..2. .1..0..1..0. .0..2..0..2
..2..1..2..2. .2..0..2..2. .0..1..1..2. .2..2..1..2. .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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