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A274749
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T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.
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11
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1, 1, 1, 2, 3, 2, 4, 8, 9, 4, 8, 22, 34, 27, 8, 16, 60, 133, 144, 81, 16, 32, 164, 518, 813, 610, 243, 32, 64, 448, 2017, 4554, 4967, 2584, 729, 64, 128, 1224, 7858, 25585, 40242, 30349, 10946, 2187, 128, 256, 3344, 30605, 143634, 327123, 355504, 185435, 46368
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OFFSET
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1,4
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COMMENTS
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Table starts
...1.....1......2........4..........8...........16............32
...1.....3......8.......22.........60..........164...........448
...2.....9.....34......133........518.........2017..........7858
...4....27....144......813.......4554........25585........143634
...8....81....610.....4967......40242.......327123.......2661918
..16...243...2584....30349.....355504......4190533......49475642
..32...729..10946...185435....3140840.....53680592.....920432562
..64..2187..46368..1133025...27748676....687685512...17123659885
.128..6561.196418..6922887..245154340...8809672678..318581114142
.256.19683.832040.42299477.2165891856.112857546696.5927090659144
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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) for n>2
k=2: a(n) = 3*a(n-1)
k=3: a(n) = 4*a(n-1) +a(n-2)
k=4: a(n) = 6*a(n-1) +a(n-2) -2*a(n-3) for n>4
k=5: a(n) = 9*a(n-1) -14*a(n-3) +10*a(n-4) -2*a(n-5) for n>6
k=6: [order 9] for n>11
k=7: [order 13] for n>15
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>2
n=2: a(n) = 2*a(n-1) +2*a(n-2)
n=3: a(n) = 2*a(n-1) +7*a(n-2) +2*a(n-3) -2*a(n-4)
n=4: [order 8]
n=5: [order 16] for n>17
n=6: [order 36] for n>38
n=7: [order 80] for n>83
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1. .0..1..0..2. .0..1..2..0. .0..1..0..2. .0..1..0..2
..1..0..1..2. .1..0..2..0. .1..2..1..2. .1..2..1..0. .1..0..1..0
..0..1..2..1. .0..1..0..2. .2..1..0..1. .2..1..0..1. .0..2..0..1
..2..0..1..2. .2..0..2..0. .0..2..1..2. .1..0..1..0. .2..0..2..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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