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A231908
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T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)
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10
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1, 1, 3, 3, 17, 9, 8, 137, 74, 27, 21, 948, 1740, 315, 81, 55, 6975, 31167, 22759, 1343, 243, 144, 50323, 614818, 1082472, 297099, 5734, 729, 377, 366170, 11900005, 57946241, 37368831, 3882566, 24495, 2187, 987, 2657785, 232002949, 3045772177
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OFFSET
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1,3
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COMMENTS
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Table starts
....1......1.........3.............8...............21...................55
....3.....17.......137...........948.............6975................50323
....9.....74......1740.........31167...........614818.............11900005
...27....315.....22759.......1082472.........57946241...........3045772177
...81...1343....297099......37368831.......5429359691.........773715251151
..243...5734...3882566....1291573433.....509273459716......196795864115357
..729..24495..50739125...44640322903...47773200503463....50062652312668838
.2187.104655.663117735.1542901809201.4481443113541663.12735271817562619233
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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)
k=2: a(n) = 6*a(n-1) -8*a(n-2) +2*a(n-3) +3*a(n-4) -a(n-5) for n>6
k=3: [order 17] for n>18
k=4: [order 81] for n>82
Empirical for row n:
n=1: a(n) = 3*a(n-1) -a(n-2) for n>3
n=2: a(n) = 9*a(n-1) -5*a(n-2) -66*a(n-3) +78*a(n-4) +4*a(n-5) -16*a(n-6)
n=3: [order 37] for n>38
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..2..1....0..0..0..1....0..2..0..1....0..2..2..1....0..0..0..0
..1..0..1..1....2..1..0..0....2..2..2..0....2..2..1..2....0..0..1..0
..0..2..0..0....1..2..2..1....2..0..0..2....2..0..0..1....1..1..0..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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