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A180986 T(n,k) = number of n X k binary matrices with rows in lexicographically nondecreasing order and columns in lexicographically nonincreasing order. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)