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A266428
T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
12
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
OFFSET
1,1
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Column 1 and row 1 are A000027(n+1).
Column 2 is A002623.
Row 2 is A004006(n+1).
Sequence in context: A227125 A248944 A267245 * A180985 A227385 A049790
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 29 2015
STATUS
approved