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A231523
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T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors
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13
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2, 2, 4, 4, 10, 8, 7, 34, 21, 16, 12, 107, 153, 48, 32, 21, 342, 865, 776, 113, 64, 37, 1069, 4665, 7697, 3861, 261, 128, 65, 3381, 25556, 70462, 66499, 18721, 601, 256, 114, 10689, 144847, 680302, 1031105, 571226, 91993, 1390, 512, 200, 33808, 817539
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OFFSET
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1,1
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COMMENTS
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Table starts
....2....2........4..........7...........12..............21................37
....4...10.......34........107..........342............1069..............3381
....8...21......153........865.........4665...........25556............144847
...16...48......776.......7697........70462..........680302...........6935963
...32..113.....3861......66499......1031105........17572772.........322599407
...64..261....18721.....571226.....15000701.......451200772.......14940780666
..128..601....91993....4944075....219937967.....11683058939......697702378939
..256.1390...453274...42759650...3222629836....302190345444....32529760276112
..512.3216..2223662..369356733..47159743290...7806399525348..1514885617016157
.1024.7435.10915727.3191749214.690399979855.201765495180944.70592106166184098
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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) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5) for n>6
k=3: [order 13] for n>14
k=4: [order 24] for n>25
k=5: [order 70] for n>71
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)
n=3: [order 16] for n>17
n=4: [order 39] for n>40
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..0..0....1..0..1..1....1..1..0..1....0..0..0..0....0..1..0..1
..1..0..0..0....0..0..0..1....1..0..0..0....0..0..0..1....1..0..0..0
..0..0..0..0....0..0..1..0....0..0..0..1....1..0..0..1....1..0..1..0
..0..1..1..1....0..0..0..0....0..1..0..0....0..0..0..1....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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