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A233098
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T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order
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13
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1, 2, 3, 5, 11, 10, 14, 65, 74, 36, 41, 386, 941, 515, 136, 122, 2315, 11486, 13721, 3602, 528, 365, 13886, 141566, 342626, 200165, 25211, 2080, 1094, 83315, 1742447, 8714705, 10221326, 2920145, 176474, 8256, 3281, 499886, 21452183, 221113913
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OFFSET
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1,2
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COMMENTS
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Table starts
......1........2............5..............14.................41
......3.......11...........65.............386...............2315
.....10.......74..........941...........11486.............141566
.....36......515........13721..........342626............8714705
....136.....3602.......200165........10221326..........537122150
....528....25211......2920145.......304926626........33113065637
...2080...176474.....42601181......9096692126......2041493495546
...8256..1235315....621496841....271376130626....125863931140721
..32896..8647202...9066845525...8095800458126...7759890074654654
.131328.60530411.132273701825.241517133090626.478420800866866973
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 6*a(n-1) -8*a(n-2)
k=2: a(n) = 8*a(n-1) -7*a(n-2)
k=3: a(n) = 16*a(n-1) -21*a(n-2) +6*a(n-3)
k=4: a(n) = 31*a(n-1) -35*a(n-2) +5*a(n-3)
k=5: [order 11]
k=6: [order 22]
Empirical for row n:
n=1: a(n) = 4*a(n-1) -3*a(n-2)
n=2: a(n) = 6*a(n-1) +a(n-2) -6*a(n-3) for n>4
n=3: a(n) = 13*a(n-1) -5*a(n-2) -47*a(n-3) +52*a(n-4) -12*a(n-5) for n>6
n=4: [order 11] for n>12
n=5: [order 27] for n>28
n=6: [order 87] for n>88
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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..1..1..0....0..1..3..3....0..1..1..0
..0..2..0..2....1..0..1..0....3..1..0..1....1..1..3..2....0..0..1..1
..3..1..0..1....0..0..0..0....0..1..1..1....3..1..0..2....0..1..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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