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A276248
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T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-2) and new values introduced in order 0..2.
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12
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1, 2, 2, 3, 9, 5, 6, 24, 36, 14, 12, 72, 85, 144, 41, 24, 216, 279, 347, 576, 122, 48, 648, 900, 1447, 1404, 2304, 365, 96, 1944, 2837, 6372, 7316, 5671, 9216, 1094, 192, 5832, 9148, 26325, 43662, 36744, 23000, 36864, 3281, 384, 17496, 29570, 115682, 234431
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OFFSET
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1,2
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COMMENTS
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Table starts
....1......2.......3........6........12..........24...........48.............96
....2......9......24.......72.......216.........648.........1944...........5832
....5.....36......85......279.......900........2837.........9148..........29570
...14....144.....347.....1447......6372.......26325.......115682.........509750
...41....576....1404.....7316.....43662......234431......1423062........8496628
..122...2304....5671....36744....291113.....2069454.....17450554......141165944
..365...9216...23000...188696...2003694....18671229....219977330.....2410124377
.1094..36864...93204...966555..13727745...167951009...2780927371....41132001645
.3281.147456..377421..4951790..93489265..1509288801..35144231606...700435484735
.9842.589824.1529844.25428687.640009243.13609728840.446083313365.11973407175492
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 4*a(n-1) for n>2
k=3: a(n) = 5*a(n-1) -4*a(n-2) +17*a(n-3) -83*a(n-4) +54*a(n-5) +56*a(n-6) for n>9
k=4: [order 36] for n>37
k=5: [order 41] for n>45
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>3
n=2: a(n) = 3*a(n-1) for n>3
n=3: [order 14] for n>15
n=4: [order 57] for n>60
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..1. .0..0..1..2. .0..0..1..1. .0..1..1..2. .0..0..1..2
..1..2..2..1. .2..0..0..1. .2..2..0..1. .2..2..0..0. .2..2..0..1
..0..1..2..2. .1..1..2..2. .0..1..2..2. .1..1..2..2. .1..1..2..2
..2..0..0..1. .0..0..1..2. .0..0..1..1. .2..0..1..1. .2..0..0..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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