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%I #4 Mar 31 2012 12:36:54
%S 0,1,1,2,8,2,4,36,36,4,12,544,3216,544,12,44,12700,257664,257664,
%T 12700,44,176,431432,69822004,464458656,69822004,431432,176,768,
%U 17482140
%N T(n,k)=Number of nXk nonnegative integer arrays with adjacent horizontal and vertical element pair sums equal to all values in 0..2nk-n-k-1 (each exactly once)
%C Table starts
%C ...0......1........2.........4.......12.....44......176.768
%C ...1......8.......36.......544....12700.431432.17482140
%C ...2.....36.....3216....257664.69822004
%C ...4....544...257664.464458656
%C ..12..12700.69822004
%C ..44.431432
%C .176
%e Some solutions for n=3 k=3
%e ..4..5..6....0..3..1....0..2..7....7..3..6....1..5..6....1..0..0....8..2..4
%e ..1..3..4....0..7..4....0..1..4....0..1..5....1..0..4....9..2..6....1..0..0
%e ..0..0..2....1..1..5....4..6..2....0..2..3....8..0..3....0..3..1....4..3..8
%Y Column 1 is A180205(n-1)
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_ Dec 27 2011