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%I #5 Mar 31 2012 12:36:45
%S 1,5,5,19,85,19,85,455,455,85,381,3617,4057,3617,381,1751,28625,48335,
%T 48335,28625,1751,8135,235827,562961,988589,562961,235827,8135,38165,
%U 1972115,7099021,20960485,20960485,7099021,1972115,38165,180325,16703881
%N T(n,k)=Number of zero-sum nXk -2..2 arrays with every element unequal to at most two horizontal and vertical neighbors
%C Table starts
%C ......1.........5.........19..........85.........381........1751..........8135
%C ......5........85........455........3617.......28625......235827.......1972115
%C .....19.......455.......4057.......48335......562961.....7099021......90062519
%C .....85......3617......48335......988589....20960485...472565771...10857153407
%C ....381.....28625.....562961....20960485...722587629.27941324053.1077779765471
%C ...1751....235827....7099021...472565771.27941324053
%C ...8135...1972115...90062519.10857153407
%C ..38165..16703881.1168520339
%C .180325.142672901
%C .856945
%H R. H. Hardin, <a href="/A201803/b201803.txt">Table of n, a(n) for n = 1..60</a>
%e Some solutions for n=4 k=3
%e .-1..1.-2....2..2.-2...-2..2..2....0..1..2....0..1..1....2..0..0....0.-1..2
%e .-1..1..1...-2..2.-2....2..2..2...-2..1..1...-1.-1..1....1..0..0....1.-1.-1
%e ..0..1..1...-2..2.-2...-2.-2.-2...-2..1..1...-1.-1.-1....1.-1.-1....1..1..1
%e ..0..0.-1...-1..2..1....1.-2.-1...-1.-1.-1....2..2.-2...-2.-1..1...-1.-1.-1
%Y Column 1 is A005191
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Dec 05 2011
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