%I #5 Mar 31 2012 12:36:25
%S 1,3,3,4,9,4,5,20,20,5,9,61,58,61,9,16,189,290,290,189,16,25,544,1217,
%T 2161,1217,544,25,39,1629,5110,14605,14605,5110,1629,39,64,4973,21969,
%U 101780,173216,101780,21969,4973,64,105,15040,93666,723029,1937895
%N T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4
%C Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 4's
%C Table starts
%C ...1.....3.......4.........5...........9............16..............25
%C ...3.....9......20........61.........189...........544............1629
%C ...4....20......58.......290........1217..........5110...........21969
%C ...5....61.....290......2161.......14605........101780..........723029
%C ...9...189....1217.....14605......173216.......1937895........21716929
%C ..16...544....5110....101780.....1937895......33962624.......608417005
%C ..25..1629...21969....723029....21716929.....608417005.....17831030743
%C ..39..4973...93666...5056631...244152037...11132866106....525537881675
%C ..64.15040..399920..35105556..2771090244..202301552532..15318916228421
%C .105.45739.1714601.245353935.31410926798.3661731514195.446553011295591
%H R. H. Hardin, <a href="/A196218/b196218.txt">Table of n, a(n) for n = 1..144</a>
%e Some solutions for n=6 k=4
%e ..0..0..2..1....0..1..1..0....1..0..2..1....0..1..1..0....1..0..0..0
%e ..1..2..1..0....2..1..1..2....1..2..1..0....0..1..1..1....1..0..0..0
%e ..1..0..1..2....1..0..0..1....0..2..1..0....1..2..0..1....1..1..2..1
%e ..1..0..1..1....1..1..2..1....0..1..1..0....2..0..0..1....0..2..2..1
%e ..2..0..2..0....0..2..0..0....0..1..2..0....1..1..1..2....0..1..1..0
%e ..1..0..1..1....1..1..0..0....1..2..0..0....0..2..1..0....0..1..2..0
%Y Column 1 is A195971
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Sep 29 2011