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A180987 T(n,k)=number of nXk binary matrices with rows in lexicographically nonincreasing order and columns in lexicographically strictly increasing order.

%I A180987 #7 Jul 22 2025 08:33:14
%S A180987 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 A180987 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 A180987 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 A180987 T(n,k)=number of nXk binary matrices with rows in lexicographically nonincreasing order and columns in lexicographically strictly increasing order.
%C A180987 Table starts
%C A180987 ..2...1...0....0....0....0.....0.....0.....0....0....0....0...0
%C A180987 ..3...3...1....0....0....0.....0.....0.....0....0....0....0...0
%C A180987 ..4...6...4....1....0....0.....0.....0.....0....0....0....0...0
%C A180987 ..5..10..10....5....1....0.....0.....0.....0....0....0....0...0
%C A180987 ..6..15..20...15....6....1.....0.....0.....0....0....0....0...0
%C A180987 ..7..21..35...35...21....7.....1.....0.....0....0....0....0...0
%C A180987 ..8..28..56...70...56...28.....8.....1.....0....0....0....0...0
%C A180987 ..9..36..84..126..126...84....36.....9.....1....0....0....0...0
%C A180987 .10..45.120..210..252..210...120....45....10....1....0....0...0
%C A180987 .11..55.165..330..462..462...330...165....55...11....1....0...0
%C A180987 .12..66.220..495..792..924...792...495...220...66...12....1...0
%C A180987 .13..78.286..715.1287.1716..1716..1287...715..286...78...13...1
%C A180987 .14..91.364.1001.2002.3003..3432..3003..2002.1001..364...91..14
%C A180987 .15.105.455.1365.3003.5005..6435..6435..5005.3003.1365..455.105
%C A180987 .16.120.560.1820.4368.8008.11440.12870.11440.8008.4368.1820.560
%H A180987 R. H. Hardin, <a href="/A180987/b180987.txt">Table of n, a(n) for n=1..478</a>
%F A180987 Conjecture: T(n,k) = A180986(n-k+1,k), k<=n . [From _R. J. Mathar_, Oct 18 2010]
%e A180987 All solutions for 3X3
%e A180987 ..0..1..1....0..1..1....0..1..1....1..1..1
%e A180987 ..0..0..1....0..0..1....0..1..1....0..1..1
%e A180987 ..0..0..0....0..0..1....0..0..1....0..0..1
%K A180987 nonn,tabl
%O A180987 1,1
%A A180987 _R. H. Hardin_ Sep 30 2010