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A239537
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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order
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13
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1, 2, 1, 6, 2, 6, 16, 6, 24, 13, 44, 16, 216, 68, 47, 120, 44, 1536, 1014, 406, 128, 328, 120, 11616, 11108, 13254, 1584, 405, 896, 328, 86400, 131988, 293741, 98304, 7790, 1181, 2448, 896, 645504, 1533792, 7199001, 3785280, 984150, 33630, 3598, 6688, 2448
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OFFSET
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1,2
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COMMENTS
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Table starts
.....1......2.........6...........16..............44...............120
.....1......2.........6...........16..............44...............120
.....6.....24.......216.........1536...........11616.............86400
....13.....68......1014........11108..........131988...........1533792
....47....406.....13254.......293741.........7199001.........171712936
...128...1584.....98304......3785280.......165336096........6976042240
...405...7790....984150.....71388971......5988724293......482858009716
..1181..33630...8368566...1093269814....169350916116....25030781490504
..3598.156032..77673624..18727824939...5466853947751..1514104924173186
.10705.695344.687582150.301846514891.164296850179323.84271877225127052
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +4*a(n-2) -3*a(n-3)
k=2: [order 10]
k=3: a(n) = 8*a(n-1) +26*a(n-2) -166*a(n-3) +96*a(n-4) +198*a(n-5) -81*a(n-6)
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2)
n=2: a(n) = 2*a(n-1) +2*a(n-2)
n=3: a(n) = 6*a(n-1) +12*a(n-2) -8*a(n-3)
n=4: [order 10]
n=5: [order 37]
n=6: [order 85]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..0..1....0..1..2..1..2....0..1..1..2..1....0..1..2..0..2
..0..1..0..0..1....0..1..2..1..2....0..1..1..2..1....0..1..2..0..2
..0..2..0..2..1....1..2..2..1..2....0..1..1..0..1....0..1..2..0..2
..0..2..0..2..1....1..2..2..1..0....2..0..2..0..2....1..0..2..1..2
..0..2..0..2..1....1..2..2..1..0....2..0..2..0..2....1..0..2..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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