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A266428
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T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
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12
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2, 3, 3, 4, 7, 4, 5, 14, 13, 5, 6, 25, 39, 22, 6, 7, 41, 106, 96, 34, 7, 8, 63, 259, 404, 212, 50, 8, 9, 92, 574, 1556, 1391, 433, 70, 9, 10, 129, 1170, 5365, 8764, 4383, 826, 95, 10, 11, 175, 2223, 16585, 49894, 45907, 12758, 1493, 125, 11, 12, 231, 3982, 46463, 251381
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OFFSET
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1,1
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COMMENTS
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Table starts
..2...3....4......5........6..........7............8............9
..3...7...14.....25.......41.........63...........92..........129
..4..13...39....106......259........574.........1170.........2223
..5..22...96....404.....1556.......5365........16585........46463
..6..34..212...1391.....8764......49894.......251381......1122721
..7..50..433...4383....45907.....448649......3889553.....29520031
..8..70..826..12758...223075....3825307.....59155748....798834778
..9..95.1493..34611..1005991...30555624....861030491..21325003746
.10.125.2575..88206..4224203..227542455..11809616668.546283341439
.11.161.4270.212609.16588684.1579153474.151566391972
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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 12] Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = (1/6)*n^3 + (1/2)*n^2 + (4/3)*n + 1
n=3: [polynomial of degree 6]
n=4: [polynomial of degree 11]
n=5: [polynomial of degree 19]
n=6: [polynomial of degree 33]
n=7: [polynomial of degree 57]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..0....0..0..1..1....0..0..0..1....0..0..1..1....0..0..0..1
..0..0..0..1....0..0..1..1....0..0..1..0....0..1..0..1....0..1..1..1
..0..0..1..1....1..1..0..1....0..1..1..1....0..1..1..1....0..1..1..1
..0..1..0..1....1..1..1..0....1..1..0..0....1..1..1..0....1..0..0..1
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CROSSREFS
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Column 1 and row 1 are A000027(n+1).
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KEYWORD
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AUTHOR
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STATUS
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approved
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