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%I #5 Mar 31 2012 12:35:56
%S 1,1,1,1,2,1,1,1,1,1,1,2,7,2,1,1,1,1,1,1,1,1,2,1,18,1,2,1,1,1,7,1,1,7,
%T 1,1,1,2,1,2,31,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,7,18,1,98,1,18,7,2,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,127,2,1,2,1,2,1,1,1,7,1,31,7,1,1,7,31,1,7
%N T(n,k)=Half the number of nXk toroidal binary arrays with each element having the sum of its vertical neighbors equal to the sum of its horizontal neighbors
%C Half the number of solutions in 0..1 of a 1-d velocity-one wave equation utt=uxx on a periodic grid
%C Table starts
%C .1.1.1..1..1..1...1...1...1....1.1..1.1...1..1...1.1...1.1....1...1.1.1...1..1
%C .1.2.1..2..1..2...1...2...1....2.1..2.1...2..1...2.1...2.1....2...1.2.1...2..1
%C .1.1.7..1..1..7...1...1...7....1.1..7.1...1..7...1.1...7.1....1...7.1.1...7..1
%C .1.2.1.18..1..2...1..18...1....2.1.18.1...2..1..18.1...2.1...18...1.2.1..18..1
%C .1.1.1..1.31..1...1...1...1...31.1..1.1...1.31...1.1...1.1...31...1.1.1...1.31
%C .1.2.7..2..1.98...1...2...7....2.1.98.1...2..7...2.1..98.1....2...7.2.1..98..1
%C .1.1.1..1..1..1.127...1...1....1.1..1.1.127..1...1.1...1.1....1.127.1.1...1..1
%C .1.2.1.18..1..2...1.450...1....2.1.18.1...2..1.450.1...2.1...18...1.2.1.450..1
%C .1.1.7..1..1..7...1...1.511....1.1..7.1...1..7...1.1.511.1....1...7.1.1...7..1
%C .1.2.1..2.31..2...1...2...1.1922.1..2.1...2.31...2.1...2.1.1922...1.2.1...2.31
%H R. H. Hardin, <a href="/A184097/b184097.txt">Table of n, a(n) for n = 1..840</a>
%e Some solutions for 9X3
%e ..1..0..0....0..0..1....1..1..0....0..1..0....1..0..1....1..1..0....0..0..1
%e ..0..1..0....0..1..0....1..0..1....1..0..0....1..1..0....0..1..1....1..0..0
%e ..0..0..1....1..0..0....0..1..1....0..0..1....0..1..1....1..0..1....0..1..0
%e ..1..0..0....0..0..1....1..1..0....0..1..0....1..0..1....1..1..0....0..0..1
%e ..0..1..0....0..1..0....1..0..1....1..0..0....1..1..0....0..1..1....1..0..0
%e ..0..0..1....1..0..0....0..1..1....0..0..1....0..1..1....1..0..1....0..1..0
%e ..1..0..0....0..0..1....1..1..0....0..1..0....1..0..1....1..1..0....0..0..1
%e ..0..1..0....0..1..0....1..0..1....1..0..0....1..1..0....0..1..1....1..0..0
%e ..0..0..1....1..0..0....0..1..1....0..0..1....0..1..1....1..0..1....0..1..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Jan 09 2011
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