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%I
%S 0,1,1,1,9,1,5,63,63,5,1,413,765,413,1,23,3293,26003,26003,3293,23,25,
%T 25123,559115,2171313,559115,25123,25,97,196811,16513425,184247585,
%U 184247585,16513425,196811,97,155,1610765,435630965,16910703303
%N T(n,k)=Number of zero-sum nXk -2..2 arrays with every element equal to at least one horizontal or vertical neighbor
%C Table starts
%C ..0......1........1.........5.........1..........23........25......97.155
%C ..1......9.......63.......413......3293.......25123....196811.1610765
%C ..1.....63......765.....26003....559115....16513425.435630965
%C ..5....413....26003...2171313.184247585.16910703303
%C ..1...3293...559115.184247585
%C .23..25123.16513425
%C .25.196811
%C .97
%e Some solutions for n=4 k=3
%e ..0..0..0....0..0..2...-2.-2.-2....2..0..0...-2..0..1....2..2..2...-2..0..0
%e ..0..0..0....0..0..2...-2.-2..1....2.-2..0...-2..0..1....2.-1.-1...-2.-1.-1
%e ..2..2.-2....1.-1.-2....1..1..1....1.-2.-2....2..2.-1....0.-1.-1....1..2..0
%e ..2.-2.-2....1.-1.-2....2..2..2....1..0..0....0..0.-1....0.-2.-2....1..2..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Dec 06 2011
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