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A232065
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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 vertically, with no adjacent values equal
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8
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1, 2, 2, 4, 6, 4, 6, 14, 14, 6, 10, 30, 46, 30, 10, 16, 66, 130, 130, 66, 16, 26, 146, 410, 534, 410, 146, 26, 42, 322, 1194, 2230, 2230, 1194, 322, 42, 68, 710, 3722, 9310, 13538, 9310, 3722, 710, 68, 110, 1566, 10942, 38870, 75462, 75462, 38870, 10942, 1566, 110
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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
...2....6.....14......30.......66........146.........322...........710
...4...14.....46.....130......410.......1194........3722.........10942
...6...30....130.....534.....2230.......9310.......38870........162278
..10...66....410....2230....13538......75462......457234.......2561258
..16..146...1194....9310....75462.....612364.....4990482......40661766
..26..322...3722...38870...457234....4990482....59448262.....653375842
..42..710..10942..162278..2561258...40661766...653375842...10508498862
..68.1566..33806..677510.15454594..331554282..7789998594..169516703810
.110.3454.100142.2828606.86936482.2703411654.85859588738.2735194512174
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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) +a(n-2) for n>3
k=2: a(n) = 2*a(n-1) +a(n-3)
k=3: a(n) = a(n-1) +7*a(n-2) -3*a(n-3) +3*a(n-4) -7*a(n-5) +2*a(n-6) -2*a(n-7) +2*a(n-8)
k=4: a(n) = 4*a(n-1) +a(n-2) -4*a(n-4) -3*a(n-5) +a(n-7) +3*a(n-8) -a(n-11)
k=5: [order 20] for n>22
k=6: [order 42]
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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..0..1..0....2..1..2..1....1..2..1..2
..1..0..1..2....1..2..1..2....0..1..2..1....1..0..1..2....0..1..0..1
..0..1..0..1....2..1..2..1....1..0..1..2....0..1..2..1....1..0..1..2
..1..2..1..2....1..0..1..0....2..1..2..1....1..0..1..2....2..1..2..1
..2..1..2..1....2..1..2..1....1..0..1..0....2..1..2..1....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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