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A240783
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T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order
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12
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1, 1, 2, 1, 3, 4, 1, 4, 11, 8, 1, 6, 20, 34, 16, 1, 9, 46, 97, 111, 32, 1, 14, 97, 305, 459, 361, 64, 1, 22, 216, 959, 2167, 2187, 1172, 128, 1, 35, 472, 3033, 10150, 15332, 10442, 3809, 256, 1, 56, 1043, 9581, 47920, 106411, 108509, 49861, 12377, 512, 1, 90, 2296, 30354
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OFFSET
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1,3
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COMMENTS
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Table starts
...1.....1.......1........1..........1...........1.............1..............1
...2.....3.......4........6..........9..........14............22.............35
...4....11......20.......46.........97.........216...........472...........1043
...8....34......97......305........959........3033..........9581..........30354
..16...111.....459.....2167......10150.......47920........226532........1071982
..32...361....2187....15332.....106411......746346.......5228820.......36701371
..64..1172...10442...108509....1120383....11677893.....121621207.....1269199948
.128..3809...49861...767834...11791412...182610635....2827515311....43857418181
.256.12377..238068..5434887..124095989..2856212777...65742420202..1515928067679
.512.40218.1136678.38467875.1306056075.44672652785.1528546759636.52397680462958
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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) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) -a(n-3) +4*a(n-4) -4*a(n-5) -3*a(n-6) +a(n-7)
k=4: [order 22]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) -a(n-3)
n=3: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-5)
n=4: [order 15]
n=5: [order 30] for n>34
n=6: [order 94]
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..1..0....0..1..1..0
..1..0..1..0....0..0..1..0....0..1..1..0....1..1..1..0....0..1..1..1
..0..0..1..0....1..0..1..1....1..1..1..0....1..1..1..0....1..0..1..1
..0..1..0..1....1..0..1..1....1..1..0..1....0..1..0..1....1..0..1..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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