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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 (list; table; graph; refs; listen; history; text; internal format)
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

R. H. Hardin, Table of n, a(n) for n = 1..145

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

Adjacent sequences:  A266425 A266426 A266427 * A266429 A266430 A266431

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 29 2015

STATUS

approved

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Last modified September 28 05:33 EDT 2020. Contains 337392 sequences. (Running on oeis4.)