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A279134
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T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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7
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0, 1, 1, 0, 0, 0, 3, 9, 9, 3, 3, 34, 66, 34, 3, 9, 87, 256, 256, 87, 9, 15, 194, 820, 1324, 820, 194, 15, 31, 400, 2551, 6396, 6396, 2551, 400, 31, 57, 790, 7491, 30074, 47452, 30074, 7491, 790, 57, 108, 1511, 21131, 129264, 316516, 316516, 129264, 21131, 1511, 108
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OFFSET
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1,7
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COMMENTS
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Table starts
...0....1......0.......3.........3...........9...........15.............31
...1....0......9......34........87.........194..........400............790
...0....9.....66.....256.......820........2551.........7491..........21131
...3...34....256....1324......6396.......30074.......129264.........535814
...3...87....820....6396.....47452......316516......2017028.......12376570
...9..194...2551...30074....316516.....3125600.....29410145......266502710
..15..400...7491..129264...2017028....29410145....409061044.....5488392521
..31..790..21131..535814..12376570...266502710...5488392521...109117856920
..57.1511..57971.2150797..73672888..2346800921..71618045798..2111166039927
.108.2830.155551.8418336.428568648.20197483932.913912909445.39962431131266
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
k=2: [order 8] for n>9
k=3: [order 11] for n>17
k=4: [order 43] for n>50
k=5: [order 88] for n>108
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..0
..1..0..1..1. .1..1..1..0. .0..0..1..0. .1..0..1..0. .1..1..0..1
..1..1..0..0. .0..0..0..1. .0..1..0..0. .0..1..1..0. .1..0..1..0
..1..0..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..0. .0..0..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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