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A231037
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T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero
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11
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0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 10, 0, 0, 0, 0, 72, 32, 2, 0, 0, 32, 736, 1344, 278, 12, 0, 0, 80, 9726, 17984, 20250, 2988, 18, 0, 0, 560, 96882, 677204, 783848, 375620, 23058, 56, 0, 0, 2080, 1194032, 18856728, 79772488, 36327118, 6620496, 199272, 170, 0, 0
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OFFSET
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1,9
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COMMENTS
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Table starts
.0..0......0.........0...........0...............0...............0
.0..0......0.........4...........0..............32..............80
.0..2.....10........72.........736............9726...........96882
.0..0.....32......1344.......17984..........677204........18856728
.0..2....278.....20250......783848........79772488......5472540636
.0.12...2988....375620....36327118.....10140483166...1844073908022
.0.18..23058...6620496..1587011224...1171740348034.555813932009140
.0.56.199272.114765278.69795938150.139409083454936
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LINKS
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FORMULA
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Empirical for column k:
k=2: a(n) = 2*a(n-1) +a(n-2) +4*a(n-3) -4*a(n-4)
k=3: [order 9]
k=4: [order 37]
Empirical for row n:
n=2: a(n) = 3*a(n-1) +6*a(n-2) +32*a(n-4) -20*a(n-5) +24*a(n-6) -16*a(n-7)
n=3: [order 33] for n>34
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EXAMPLE
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Some solutions for n=3 k=4
..0..1..0..1....0..1..1..0....0..2..1..0....0..2..0..2....0..1..0..1
..1..2..2..2....2..2..2..0....0..1..2..0....1..1..1..0....1..2..2..0
..1..0..1..0....1..0..1..0....0..2..1..0....2..0..2..0....1..0..1..0
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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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