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

1,1

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

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]

Example

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

Crossrefs

Sequence in context: A239621 A349444 A231204 * A092093 A197386 A357991

Adjacent sequences: A180984 A180985 A180986 * A180988 A180989 A180990

Keyword

nonn,tabl

Author

R. H. Hardin Sep 30 2010

Status

approved