A180986 T(n,k) = number of n X k binary matrices with rows in lexicographically nondecreasing order and columns in lexicographically nonincreasing order.

2, 3, 3, 4, 6, 4, 5, 10, 10, 5, 6, 15, 20, 15, 6, 7, 21, 35, 35, 21, 7, 8, 28, 56, 70, 56, 28, 8, 9, 36, 84, 126, 126, 84, 36, 9, 10, 45, 120, 210, 252, 210, 120, 45, 10, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 13, 78, 286, 715

Offset: 1

Author

R. H. Hardin, Sep 30 2010

Keywords

• nonn
• tabl

Comments

Table starts:

..2..3...4....5....6....7.....8.....9....10.....11.....12.....13......14

..3..6..10...15...21...28....36....45....55.....66.....78.....91.....105

..4.10..20...35...56...84...120...165...220....286....364....455.....560

..5.15..35...70..126..210...330...495...715...1001...1365...1820....2380

..6.21..56..126..252..462...792..1287..2002...3003...4368...6188....8568

..7.28..84..210..462..924..1716..3003..5005...8008..12376..18564...27132

..8.36.120..330..792.1716..3432..6435.11440..19448..31824..50388...77520

..9.45.165..495.1287.3003..6435.12870.24310..43758..75582.125970..203490

.10.55.220..715.2002.5005.11440.24310.48620..92378.167960.293930..497420

.11.66.286.1001.3003.8008.19448.43758.92378.184756.352716.646646.1144066

Is this (apart from offsets and formatting) the same sequence as A014410? [R. J. Mathar, Oct 02 2010]

Yes, because it obeys the recursion formula for binomial coefficients: the top left element is either 0 (leaving T(n-1,k) ways to fill the rest) or 1 (leaving T(n,k-1) ways to fill the rest). [Karl W. Heuer, Aug 25 2014]

Examples

			All solutions for 3 X 3:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..0..0....0..0..0....1..0..0....1..0..0....1..1..0....1..0..0
..1..0..0....1..1..0....1..1..1....1..0..0....1..1..0....1..1..0....1..1..1
...
..0..0..0....0..0..0....1..0..0....1..0..0....1..0..0....1..0..0....1..0..0
..1..1..0....1..1..1....1..0..0....1..0..0....1..1..0....1..0..0....1..1..0
..1..1..1....1..1..1....1..0..0....1..1..0....1..1..0....1..1..1....1..1..1
...
..1..0..0....1..1..0....1..1..0....1..1..0....1..1..1....0..0..0
..1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....0..0..0
..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..544

Crossrefs

A014410 is the same sequence viewed as a triangle.