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A279856
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T(n,k)=Number of nXk 0..2 arrays with no element unequal 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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6
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0, 0, 0, 2, 4, 2, 2, 10, 10, 2, 8, 24, 49, 24, 8, 14, 54, 168, 168, 54, 14, 36, 116, 557, 972, 557, 116, 36, 74, 250, 1758, 5200, 5200, 1758, 250, 74, 168, 528, 5441, 26632, 44893, 26632, 5441, 528, 168, 358, 1118, 16500, 134898, 373516, 373516, 134898, 16500
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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..........8..........14..........36..........74
...0....4.....10.......24.........54.........116.........250.........528
...2...10.....49......168........557........1758........5441.......16500
...2...24....168......972.......5200.......26632......134898......668668
...8...54....557.....5200......44893......373516.....3010179....23836450
..14..116...1758....26632.....373516.....4989784....64921744...827573664
..36..250...5441...134898....3010179....64921744..1356293555.27796618392
..74..528..16500...668668...23836450...827573664.27796618392
.168.1118..49253..3278294..185854745.10392951988
.358.2348.145290.15902088.1432781380
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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) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5
k=2: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5)
k=3: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-4) -4*a(n-5) -4*a(n-6) for n>9
k=4: [order 38] for n>41
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
..0..1..1..1. .0..0..1..1. .0..0..0..1. .1..1..0..1. .0..0..0..1
..2..2..1..1. .0..2..2..1. .2..0..0..1. .1..1..0..0. .0..0..0..1
..2..2..2..2. .0..2..2..1. .0..0..0..1. .0..0..0..0. .0..0..1..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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