A266362 T(n,k) = Number of n X k binary arrays with rows and columns lexicographically nondecreasing and row and column sums nondecreasing.

2, 3, 3, 4, 7, 4, 5, 13, 13, 5, 6, 22, 35, 22, 6, 7, 34, 82, 82, 34, 7, 8, 50, 173, 276, 173, 50, 8, 9, 70, 337, 830, 830, 337, 70, 9, 10, 95, 614, 2278, 3669, 2278, 614, 95, 10, 11, 125, 1060, 5752, 14921, 14921, 5752, 1060, 125, 11, 12, 161, 1749, 13525, 55734, 93085

Offset: 1

Author

R. H. Hardin, Dec 28 2015

Keywords

• nonn
• tabl

Comments

Table starts

..2...3....4.....5.......6........7..........8..........9.........10.........11

..3...7...13....22......34.......50.........70.........95........125........161

..4..13...35....82.....173......337........614.......1060.......1749.......2777

..5..22...82...276.....830.....2278.......5752......13525......29864......62455

..6..34..173...830....3669....14921......55734.....191916.....612871....1827072

..7..50..337..2278...14921....93085.....541207....2909244...14424728...66153106

..8..70..614..5752...55734...541207....5061414...44435916..361401441.2711340372

..9..95.1060.13525..191916..2909244...44435916..654427939.9043864160

.10.125.1749.29864..612871.14424728..361401441.9043864160

.11.161.2777.62455.1827072.66153106.2711340372

Examples

			Some solutions for n=4, k=4
..0..0..0..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..0..0
..0..0..1..1....0..0..0..1....0..1..0..1....0..1..1..1....0..0..0..1
..0..1..1..0....1..1..1..0....0..1..1..1....1..1..0..1....0..1..1..0
..1..0..0..1....1..1..1..0....1..1..1..0....1..1..1..1....0..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..143

Crossrefs

Column 1 is A000027(n+1).

Column 2 is A002623.

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: a(n) = 5*a(n-1) -9*a(n-2) +6*a(n-3) -6*a(n-7) +9*a(n-8) -5*a(n-9) +a(n-10).