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A201503
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T(n,k)=Number of nXk 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
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5
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2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 3, 6, 3, 2, 1, 3, 5, 5, 3, 1, 2, 4, 12, 8, 12, 4, 2, 1, 4, 8, 12, 12, 8, 4, 1, 2, 5, 20, 18, 40, 18, 20, 5, 2, 1, 5, 13, 24, 32, 32, 24, 13, 5, 1, 2, 6, 30, 33, 98, 58, 98, 33, 30, 6, 2, 1, 6, 18, 43, 73, 94, 94, 73, 43, 18, 6, 1, 2, 7, 42, 55, 204, 151, 338, 151, 204
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OFFSET
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1,1
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COMMENTS
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Table starts
.2.1..2..1...2...1...2....1....2....1....2.....1.....2.....1.....2......1
.1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9
.2.2..6..5..12...8..20...13...30...18...42....25....56....32....72.....41
.1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177
.2.3.12.12..40..32..98...73..204..141..380...252...650...414..1042....649
.1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137
.2.4.20.24..98..94.338..289..936..734.2234..1656..4770..3370..9344...6375
.1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575
.2.5.30.43.204.227.936..910.3334.2934.9936..8150.25908.20094.60882..45207
.1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583
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LINKS
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..1
..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1
..0..1..1..1....0..1..1..1....0..0..1..1....1..1..1..1....0..0..1..1
..0..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1....1..1..1..1
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CROSSREFS
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Column 3 odd terms are A002378((n+1)/2)
Column 3 even terms are A000982((n+2)/2)
Column 5 even terms are A188183((n-2)/2)
Column 7 even terms are A188185((n-4)/2)
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KEYWORD
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AUTHOR
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STATUS
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approved
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