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A266547 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.

%I A266547 #4 Dec 31 2015 07:07:35
%S A266547 2,2,2,2,3,2,2,3,3,2,2,4,5,4,2,2,4,6,6,4,2,2,5,8,12,8,5,2,2,5,11,16,
%T A266547 16,11,5,2,2,6,13,27,36,27,13,6,2,2,6,16,36,58,58,36,16,6,2,2,7,20,57,
%U A266547 110,176,110,57,20,7,2,2,7,23,76,196,366,366,196,76,23,7,2,2,8,27,114,363
%N A266547 T(n,k)=Number of nXk binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.
%C A266547 Table starts
%C A266547 .2.2..2...2...2....2......2.......2........2........2........2........2.......2
%C A266547 .2.3..3...4...4....5......5.......6........6........7........7........8.......8
%C A266547 .2.3..5...6...8...11.....13......16.......20.......23.......27.......32......36
%C A266547 .2.4..6..12..16...27.....36......57.......76......114......149......213.....276
%C A266547 .2.4..8..16..36...58....110.....196......363......695.....1157.....2023....3446
%C A266547 .2.5.11..27..58..176....366....1062.....2571.....7345....17540....47970..109375
%C A266547 .2.5.13..36.110..366...1688....5312....24921...101495...417118..1673507.6081357
%C A266547 .2.6.16..57.196.1062...5312...48167...264355..2251914.13562215.97760446
%C A266547 .2.6.20..76.363.2571..24921..264355..4283651.40874990
%C A266547 .2.7.23.114.695.7345.101495.2251914.40874990
%H A266547 R. H. Hardin, <a href="/A266547/b266547.txt">Table of n, a(n) for n = 1..179</a>
%F A266547 Empirical for column k:
%F A266547 k=1: a(n) = a(n-1)
%F A266547 k=2: a(n) = a(n-1) +a(n-2) -a(n-3)
%F A266547 k=3: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -2*a(n-4) +a(n-5)
%F A266547 k=4: [order 17]
%e A266547 Some solutions for n=6 k=4
%e A266547 ..0..0..1..1....0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1
%e A266547 ..0..1..0..1....0..1..0..0....0..0..1..0....0..0..1..1....0..0..1..1
%e A266547 ..1..0..1..0....1..0..0..0....0..1..0..0....0..0..1..1....1..1..0..0
%e A266547 ..1..1..0..0....1..0..0..0....0..1..0..0....1..1..0..0....1..1..0..0
%e A266547 ..1..1..0..0....1..0..0..0....1..0..0..0....1..1..0..0....1..1..0..0
%e A266547 ..1..1..0..0....1..0..0..0....1..0..0..0....1..1..0..0....1..1..0..0
%Y A266547 Column 2 is A004526(n+4).
%K A266547 nonn,tabl
%O A266547 1,1
%A A266547 _R. H. Hardin_, Dec 31 2015