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A231839
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T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors
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14
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4, 4, 16, 16, 50, 64, 50, 188, 422, 256, 144, 760, 4508, 3823, 1024, 422, 3309, 52411, 111621, 34350, 4096, 1268, 14666, 678660, 3477361, 2836554, 308419, 16384, 3823, 64607, 8887871, 124132900, 241961326, 71178861, 2771101, 65536, 11472, 283479
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OFFSET
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1,1
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COMMENTS
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Table starts
.......4..........4.............16.................50....................144
......16.........50............188................760...................3309
......64........422...........4508..............52411.................678660
.....256.......3823.........111621............3477361..............124132900
....1024......34350........2836554..........241961326............24188209253
....4096.....308419.......71178861........16599585680..........4666623161419
...16384....2771101.....1792092360......1140658285204........899426070636904
...65536...24892609....45099279326.....78428361897720.....173546274977761257
..262144..223618304..1134900171250...5390322528656652...33474310504831841795
.1048576.2008825312.28560684486812.370517687958114665.6456965889651937136227
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1)
k=2: a(n) = 4*a(n-1) +34*a(n-2) +86*a(n-3) +91*a(n-4) +46*a(n-5) +11*a(n-6) +a(n-7)
k=3: [order 10] for n>11
k=4: [order 29] for n>30
k=5: [order 82] for n>83
Empirical for row n:
n=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8
n=2: [order 31] for n>32
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EXAMPLE
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Some solutions for n=3 k=4
..3..2..2..2....2..2..3..2....2..2..0..0....3..3..1..0....0..0..0..3
..0..0..3..0....2..3..2..2....3..0..0..1....2..1..0..0....0..0..1..1
..0..0..0..1....2..2..2..3....1..2..2..2....1..1..1..2....2..2..2..2
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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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