A266428 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

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

Author

R. H. Hardin, Dec 29 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 and row 1 are A000027(n+1).

Column 2 is A002623.

Row 2 is A004006(n+1).

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]