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A251317
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements
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9
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10, 25, 25, 61, 79, 61, 149, 238, 238, 149, 365, 720, 890, 720, 365, 894, 2199, 3369, 3369, 2199, 894, 2189, 6717, 12859, 16006, 12859, 6717, 2189, 5360, 20484, 48980, 76167, 76167, 48980, 20484, 5360, 13125, 62464, 186162, 361845, 451826, 361845
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OFFSET
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1,1
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COMMENTS
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Table starts
....10.....25.......61.......149........365.........894..........2189
....25.....79......238.......720.......2199........6717.........20484
....61....238......890......3369......12859.......48980........186162
...149....720.....3369.....16006......76167......361845.......1720147
...365...2199....12859.....76167.....451826.....2688099......16024915
...894...6717....48980....361845....2688099....20080487.....149982413
..2189..20484...186162...1720147...16024915...149982413....1401489913
..5360..62464...707897...8186775...95495471..1118147932...13088358653
.13125.190542..2693783..38968823..568712168..8339278058..122472226217
.32139.581259.10250631.185439356.3387770571.62282522930.1147464543755
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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) -2*a(n-2) +2*a(n-3) -a(n-4)
k=2: a(n) = 5*a(n-1) -9*a(n-2) +13*a(n-3) -13*a(n-4) +6*a(n-5) -2*a(n-6)
k=3: [order 10]
k=4: [order 15] for n>17
k=5: [order 26] for n>27
k=6: [order 42] for n>44
k=7: [order 68] for n>70
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..0..0..1....1..1..1..0..0....0..1..1..0..0....1..1..0..1..1
..0..1..0..0..1....0..0..1..1..0....1..0..1..1..0....0..1..0..0..1
..0..1..0..0..0....1..0..0..1..1....1..1..0..1..1....0..1..0..0..0
..0..1..1..1..1....1..0..0..0..1....0..1..0..0..1....0..1..1..0..0
..0..0..0..0..1....1..1..1..0..0....0..1..0..0..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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