A180987 - OEIS

%I #5 Mar 31 2012 12:35:49

%S 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,

%T 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,

%U 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

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

%C Table starts

%C ..2...1...0....0....0....0.....0.....0.....0....0....0....0...0

%C ..3...3...1....0....0....0.....0.....0.....0....0....0....0...0

%C ..4...6...4....1....0....0.....0.....0.....0....0....0....0...0

%C ..5..10..10....5....1....0.....0.....0.....0....0....0....0...0

%C ..6..15..20...15....6....1.....0.....0.....0....0....0....0...0

%C ..7..21..35...35...21....7.....1.....0.....0....0....0....0...0

%C ..8..28..56...70...56...28.....8.....1.....0....0....0....0...0

%C ..9..36..84..126..126...84....36.....9.....1....0....0....0...0

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

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

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

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

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

%C .15.105.455.1365.3003.5005..6435..6435..5005.3003.1365..455.105

%C .16.120.560.1820.4368.8008.11440.12870.11440.8008.4368.1820.560

%H R. H. Hardin, <a href="/A180987/b180987.txt">Table of n, a(n) for n=1..478</a>

%F Conjecture: T(n,k) = A180986(n-k+1,k), k<=n . [From _R. J. Mathar_, Oct 18 2010]

%e All solutions for 3X3

%e ..0..1..1....0..1..1....0..1..1....1..1..1

%e ..0..0..1....0..0..1....0..1..1....0..1..1

%e ..0..0..0....0..0..1....0..0..1....0..0..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Sep 30 2010