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A232515
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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, diagonally or antidiagonally, with no adjacent elements equal
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16
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4, 16, 4, 16, 52, 8, 54, 32, 200, 16, 74, 326, 128, 784, 28, 218, 250, 2516, 400, 3052, 52, 340, 2138, 1730, 19138, 1344, 11900, 96, 868, 1956, 32084, 10118, 145682, 4416, 46432, 176, 1494, 13976, 24388, 475086, 64290, 1110752, 14608, 181184, 324, 3528
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OFFSET
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1,1
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COMMENTS
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Table starts
...4......16.....16.........54........74...........218..........340
...4......52.....32........326.......250..........2138.........1956
...8.....200....128.......2516......1730.........32084........24388
..16.....784....400......19138.....10118........475086.......270400
..28....3052...1344.....145682.....64290.......7059918......3267824
..52...11900...4416....1110752....399122.....105188684.....38988416
..96...46432..14608....8470018...2523098....1567758430....476578496
.176..181184..48224...64594290..15907690...23370338858...5831607392
.324..707044.159296..492627324.100603770..348398002228..71731172848
.596.2759212.526096.3757052022.636270550.5193906376594.883465590796
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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) +a(n-3)
k=2: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) -5*a(n-4) -2*a(n-5) +a(n-6) +2*a(n-7)
k=3: a(n) = 2*a(n-1) +4*a(n-2) +a(n-3)
k=4: [order 14]
k=5: [order 18] for n>19
k=6: [order 49]
k=7: [order 78]
Empirical for row n:
n=1: a(n) = 3*a(n-2) +a(n-3) +2*a(n-4) +2*a(n-5)
n=2: a(n) = 6*a(n-2) +a(n-3) +3*a(n-4) +a(n-5) -2*a(n-6) -2*a(n-7)
n=3: [order 9]
n=4: [order 23]
n=5: [order 42]
n=6: [order 90]
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..2..1..0....0..1..2..1..2....0..1..0..1..0....2..1..0..1..0
..0..1..2..1..0....0..1..2..1..0....2..1..2..1..0....2..1..2..1..2
..2..1..2..1..0....0..1..0..1..2....2..1..0..1..0....2..1..2..1..2
..2..1..0..1..2....0..1..0..1..0....2..1..2..1..2....2..1..0..1..0
..2..1..2..1..2....0..1..2..1..0....2..1..2..1..0....2..1..0..1..2
..0..1..0..1..0....2..1..0..1..0....0..1..2..1..2....0..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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