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A215292
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T(n,k)=Number of permutations of 0..floor((n*k-1)/2) on even squares of an nXk array such that each row and column of even squares is increasing
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8
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 10, 6, 1, 1, 10, 30, 30, 10, 1, 1, 20, 140, 280, 140, 20, 1, 1, 35, 420, 2100, 2100, 420, 35, 1, 1, 70, 2310, 23100, 60060, 23100, 2310, 70, 1, 1, 126, 6930, 210210, 1051050, 1051050, 210210, 6930, 126, 1, 1, 252, 42042, 2522520
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1.....1........1...........1..............1..................1
.1...2.....3........6..........10.............20.................35
.1...3....10.......30.........140............420...............2310
.1...6....30......280........2100..........23100.............210210
.1..10...140.....2100.......60060........1051050...........42882840
.1..20...420....23100.....1051050.......85765680.........5703417720
.1..35..2310...210210....42882840.....5703417720......2061378118800
.1..70..6930..2522520...814773960...577185873264....337653735859440
.1.126.42042.25729704.41227562376.48236247979920.173457547735792320
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LINKS
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FORMULA
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f1=floor((k+1)/2)
f2=floor(k/2)
f3=floor((n+1)/2)
f4=floor(n/2)
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EXAMPLE
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Some solutions for n=5 k=4
..1..x..2..x....0..x..6..x....1..x..6..x....1..x..4..x....0..x..6..x
..x..0..x..4....x..3..x..4....x..0..x..3....x..0..x..3....x..1..x..2
..3..x..8..x....1..x..7..x....4..x..7..x....2..x..7..x....4..x..7..x
..x..6..x..7....x..5..x..8....x..2..x..8....x..5..x..6....x..3..x..9
..5..x..9..x....2..x..9..x....5..x..9..x....8..x..9..x....5..x..8..x
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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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