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A279268
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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 one element, and with new values introduced in order 0 sequentially upwards.
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7
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0, 0, 0, 2, 4, 2, 2, 10, 10, 2, 5, 20, 29, 20, 5, 8, 38, 86, 86, 38, 8, 15, 68, 240, 400, 240, 68, 15, 26, 120, 626, 1592, 1592, 626, 120, 26, 46, 208, 1603, 5888, 9042, 5888, 1603, 208, 46, 80, 358, 4030, 21882, 51568, 51568, 21882, 4030, 358, 80, 139, 612, 9973, 79112
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OFFSET
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1,4
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COMMENTS
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Table starts
..0...0.....2......2........5..........8..........15............26
..0...4....10.....20.......38.........68.........120...........208
..2..10....29.....86......240........626........1603..........4030
..2..20....86....400.....1592.......5888.......21882.........79112
..5..38...240...1592.....9042......51568......283450.......1526492
..8..68...626...5888....51568.....429716.....3490152......27850092
.15.120..1603..21882...283450....3490152....42093113.....498160278
.26.208..4030..79112..1526492...27850092...498160278....8746623144
.46.358..9973.281754..8110769..218952412..5812405127..151499712450
.80.612.24388.991292.42557410.1701805320.67071788240.2595668095672
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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) +a(n-2) -2*a(n-3) -a(n-4) for n>5
k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
k=3: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-3) -4*a(n-4) -a(n-6) for n>9
k=4: [order 28] for n>31
k=5: [order 58] for n>69
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..1..0..0. .0..1..0..1
..1..0..0..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..1..0
..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..0. .1..0..1..0
..0..1..1..0. .1..0..1..0. .1..1..0..0. .0..1..0..1. .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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