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A232335
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T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal
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12
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1, 2, 1, 4, 6, 1, 6, 18, 16, 1, 10, 32, 74, 42, 1, 16, 82, 154, 308, 110, 1, 26, 162, 628, 734, 1282, 288, 1, 42, 388, 1470, 4906, 3472, 5338, 754, 1, 68, 806, 5530, 13170, 38986, 16338, 22228, 1974, 1, 110, 1858, 13906, 82526, 117690, 312276, 76630, 92562, 5168
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OFFSET
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1,2
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COMMENTS
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Table starts
.1.....2.......4.......6.........10.........16............26............42
.1.....6......18......32.........82........162...........388...........806
.1....16......74.....154........628.......1470..........5530.........13906
.1....42.....308.....734.......4906......13170.........82526........239992
.1...110....1282....3472......38986.....117690.......1274656.......4158066
.1...288....5338...16338.....312276....1047700......20052758......71916112
.1...754...22228...76630....2510674....9298730.....318521414....1241196022
.1..1974...92562..358656...20221026...82332898....5084744564...21383016966
.1..5168..385450.1676330..162993780..727588212...81376107850..367791626696
.1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)
k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)
k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5
k=6: [order 7] for n>9
k=7: [order 16] for n>18
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6
n=3: [order 8] for n>12
n=4: [order 21] for n>24
n=5: [order 36] for n>42
n=6: [order 80] for n>87
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EXAMPLE
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Some solutions for n=5 k=4
..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1
..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1
..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2
..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2
..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..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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