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A235884
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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
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9
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21, 51, 51, 129, 105, 129, 339, 231, 231, 339, 921, 537, 453, 537, 921, 2571, 1311, 951, 951, 1311, 2571, 7329, 3345, 2109, 1833, 2109, 3345, 7329, 21219, 8871, 4911, 3759, 3759, 4911, 8871, 21219, 62121, 24297, 11973, 8097, 7221, 8097, 11973, 24297, 62121
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OFFSET
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1,1
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COMMENTS
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Table starts
.....21.....51....129....339....921...2571...7329...21219...62121..183291
.....51....105....231....537...1311...3345...8871...24297...68271..195585
....129....231....453....951...2109...4911..11973...30471...80589..220191
....339....537....951...1833...3759...8097..18231...42873..105279..269457
....921...1311...2109...3759...7221..14631..30909...67839..154821..368151
...2571...3345...4911...8097..14631..28185..56751..118257..254391..566025
...7329...8871..11973..18231..30909..56751.109893..220551..454989..963231
..21219..24297..30471..42873..67839.118257.220551..429513..860559.1762017
..62121..68271..80589.105279.154821.254391.454989..860559.1684821.3372711
.183291.195585.220191.269457.368151.566025.963231.1762017.3372711.6633465
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LINKS
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FORMULA
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Empirical for diagonal and column k (the k=2 recurrence also works for k=1; apparently all rows and columns satisfy the same order 3 recurrence):
diagonal: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4)
k=1: a(n) = 5*a(n-1) -6*a(n-2)
k=2..7..(?): a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3)
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0..0....2..1..1..2..2....2..2..2..2..1....1..1..0..1..1
..0..0..0..0..0....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1
..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....1..1..0..1..1
..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....0..0..1..0..0
..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1
..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....0..0..1..0..0
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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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