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A301407
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 252, 128, 16, 32, 512, 1988, 1988, 512, 32, 64, 2048, 15680, 31012, 15680, 2048, 64, 128, 8192, 123676, 483600, 483600, 123676, 8192, 128, 256, 32768, 975492, 7541492, 14905344, 7541492, 975492, 32768, 256, 512, 131072
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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...........8.............16...............32
...2......8.......32.........128............512.............2048
...4.....32......252........1988..........15680...........123676
...8....128.....1988.......31012.........483600..........7541492
..16....512....15680......483600.......14905344........459428416
..32...2048...123676.....7541492......459428416......27990353344
..64...8192...975492...117605364....14160945920....1705287652128
.128..32768..7694176..1833990416...436482419456..103893157740576
.256.131072.60687676.28600063044.13453684678656.6329599807409536
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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)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +7*a(n-2)
k=4: a(n) = 13*a(n-1) +40*a(n-2) +9*a(n-3) -29*a(n-4) +4*a(n-5)
k=5: [order 8] for n>9
k=6: [order 22] for n>23
k=7: [order 45] for n>47
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
..1..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..1..1..1
..1..0..1..1. .1..1..1..0. .0..0..1..0. .1..1..0..0. .1..1..1..1
..1..1..0..0. .1..1..0..0. .1..0..1..1. .0..1..0..1. .1..0..0..0
..0..0..0..0. .1..1..1..1. .1..1..0..1. .1..1..1..1. .1..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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