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

1,1

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]

Links

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

Example

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

Crossrefs

A014410 is the same sequence viewed as a triangle.

Sequence in context: A059442 A225273 A014410 * A200763 A203291 A220053

Adjacent sequences: A180983 A180984 A180985 * A180987 A180988 A180989

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 30 2010

Status

approved