A180987 T(n,k)=number of nXk binary matrices with rows in lexicographically nonincreasing order and columns in lexicographically strictly increasing order.

2, 1, 3, 0, 3, 4, 0, 1, 6, 5, 0, 0, 4, 10, 6, 0, 0, 1, 10, 15, 7, 0, 0, 0, 5, 20, 21, 8, 0, 0, 0, 1, 15, 35, 28, 9, 0, 0, 0, 0, 6, 35, 56, 36, 10, 0, 0, 0, 0, 1, 21, 70, 84, 45, 11, 0, 0, 0, 0, 0, 7, 56, 126, 120, 55, 12, 0, 0, 0, 0, 0, 1, 28, 126, 210, 165, 66, 13, 0, 0, 0, 0, 0, 0, 8, 84, 252, 330

Offset: 1

Author

R. H. Hardin Sep 30 2010

Keywords

• nonn
• tabl

Comments

Table starts

..2...1...0....0....0....0.....0.....0.....0....0....0....0...0

..3...3...1....0....0....0.....0.....0.....0....0....0....0...0

..4...6...4....1....0....0.....0.....0.....0....0....0....0...0

..5..10..10....5....1....0.....0.....0.....0....0....0....0...0

..6..15..20...15....6....1.....0.....0.....0....0....0....0...0

..7..21..35...35...21....7.....1.....0.....0....0....0....0...0

..8..28..56...70...56...28.....8.....1.....0....0....0....0...0

..9..36..84..126..126...84....36.....9.....1....0....0....0...0

.10..45.120..210..252..210...120....45....10....1....0....0...0

.11..55.165..330..462..462...330...165....55...11....1....0...0

.12..66.220..495..792..924...792...495...220...66...12....1...0

.13..78.286..715.1287.1716..1716..1287...715..286...78...13...1

.14..91.364.1001.2002.3003..3432..3003..2002.1001..364...91..14

.15.105.455.1365.3003.5005..6435..6435..5005.3003.1365..455.105

.16.120.560.1820.4368.8008.11440.12870.11440.8008.4368.1820.560

Examples

			All solutions for 3X3
..0..1..1....0..1..1....0..1..1....1..1..1
..0..0..1....0..0..1....0..1..1....0..1..1
..0..0..0....0..0..1....0..0..1....0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..478

Formula

Conjecture: T(n,k) = A180986(n-k+1,k), k<=n . [From R. J. Mathar, Oct 18 2010]