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A266935
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T(n,k)=Number of nXk binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
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12
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2, 2, 3, 2, 4, 4, 2, 4, 7, 5, 2, 5, 9, 12, 6, 2, 5, 12, 20, 19, 7, 2, 6, 14, 35, 44, 29, 8, 2, 6, 19, 52, 100, 92, 42, 9, 2, 7, 21, 82, 210, 288, 182, 59, 10, 2, 7, 26, 115, 429, 871, 794, 340, 80, 11, 2, 8, 30, 169, 816, 2577, 3566, 2077, 605, 106, 12, 2, 8, 35, 232, 1534, 7185
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OFFSET
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1,1
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COMMENTS
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Table starts
..2...2....2.....2......2.......2........2..........2.........2.........2
..3...4....4.....5......5.......6........6..........7.........7.........8
..4...7....9....12.....14......19.......21.........26........30........35
..5..12...20....35.....52......82......115........169.......232.......322
..6..19...44...100....210.....429......816.......1534......2727......4753
..7..29...92...288....871....2577.....7185......19529.....50216....125786
..8..42..182...794...3566...15850....68890.....288333...1155281...4410923
..9..59..340..2077..13899...96503...671796....4605960..30319512.191420936
.10..80..605..5110..50841..555060..6347005...73046059.821453747
.11.106.1028.11869.173470.2977370.56180274.1104862960
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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) -a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5)
k=3: [order 11]
k=4: [order 31]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +a(n-2) -a(n-3)
n=3: a(n) = a(n-1) +a(n-2) -a(n-4) -a(n-5) +a(n-6)
n=4: [order 17]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1
..0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..0....1..1..0..0
..1..0..0..1....1..1..1..1....1..1..1..1....0..0..0..1....1..1..0..0
..1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..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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