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A283543
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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.
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12
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2, 4, 4, 7, 11, 8, 13, 27, 33, 16, 24, 76, 127, 98, 32, 44, 201, 578, 573, 291, 64, 81, 537, 2369, 4089, 2615, 865, 128, 149, 1444, 10069, 25532, 29558, 11903, 2570, 256, 274, 3859, 42664, 167920, 282773, 212441, 54211, 7637, 512, 504, 10339, 179733, 1094959
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OFFSET
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1,1
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COMMENTS
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Table starts
....2.....4.......7........13..........24............44..............81
....4....11......27........76.........201...........537............1444
....8....33.....127.......578........2369.........10069...........42664
...16....98.....573......4089.......25532........167920.........1094959
...32...291....2615.....29558......282773.......2905717........29377334
...64...865...11903....212441.....3109801......49760703.......778500603
..128..2570...54211...1529463....34266804.....854841910.....20707472573
..256..7637..246869..11006233...377393657...14672363665....550220030803
..512.22693.1124239..79212552..4156954825..251901309671..14624495679716
.1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840
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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)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)
k=4: [order 8]
k=5: [order 21]
k=6: [order 27]
k=7: [order 59]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3)
n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)
n=4: [order 8]
n=5: [order 21]
n=6: [order 32]
n=7: [order 69]
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EXAMPLE
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Some solutions for n=4 k=4
..1..1..0..0. .0..1..0..0. .1..0..0..0. .0..0..1..0. .0..1..0..0
..0..0..0..1. .0..0..1..0. .1..0..0..1. .1..0..0..1. .0..1..0..0
..0..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..1. .1..0..0..1
..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..1
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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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