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A251268
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having x11-x00 less than x10-x01
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14
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11, 26, 35, 57, 114, 108, 120, 313, 480, 337, 247, 772, 1667, 2058, 1049, 502, 1775, 4930, 9109, 8812, 3268, 1013, 3894, 13052, 32636, 49872, 37772, 10179, 2036, 8277, 31936, 100843, 217634, 273607, 161906, 31707, 4083, 17224, 73805, 279718, 790734
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OFFSET
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1,1
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COMMENTS
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Table starts
.....11.......26........57........120.........247..........502.........1013
.....35......114.......313........772........1775.........3894.........8277
....108......480......1667.......4930.......13052........31936........73805
....337.....2058......9109......32636......100843.......279718.......715685
...1049.....8812.....49872.....217634......790734......2510004......7189937
...3268....37772....273607....1457326.....6247708.....22806904.....73607411
..10179...161906...1501739....9772880....49523566....208452452....760734085
..31707...694042...8244503...65582500...393172015...1910905110...7901650053
..98764..2975162..45265163..440223510..3123669457..17543333688..82288916360
.307641.12753740.248529844.2955392154.24825649060.161181383956.858174176431
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-3)
k=2: a(n) = 5*a(n-1) -2*a(n-2) -5*a(n-3) +2*a(n-4)
k=3: [order 10]
k=4: [order 16]
k=5: [order 36]
k=6: [order 62]
Empirical for row n:
n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
n=2: a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5)
n=3: [order 8]
n=4: [order 10]
n=5: [order 12]
n=6: [order 14]
n=7: [order 16]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..0..0....0..1..1..1..1....0..0..0..0..1....0..0..1..0..1
..1..1..1..1..1....0..0..0..1..1....0..1..1..1..1....0..0..0..1..1
..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..1..1..1..1
..1..1..1..1..1....0..0..0..0..0....0..0..1..1..1....0..0..0..0..0
..0..0..0..0..1....0..0..1..1..1....0..1..0..1..1....0..0..1..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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