%I #5 Mar 31 2012 12:36:27
%S 1,1,1,2,7,2,3,10,10,3,5,23,34,23,5,8,57,104,104,57,8,13,122,386,815,
%T 386,122,13,21,275,1380,3675,3675,1380,275,21,34,623,4800,20500,31899,
%U 20500,4800,623,34,55,1394,16794,115563,260394,260394,115563,16794,1394,55,89
%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 4,3,0,2,1 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 1's
%C Table starts
%C ..1....1......2........3..........5............8............13..............21
%C ..1....7.....10.......23.........57..........122...........275.............623
%C ..2...10.....34......104........386.........1380..........4800...........16794
%C ..3...23....104......815.......3675........20500........115563..........638791
%C ..5...57....386.....3675......31899.......260394.......2246059........19246379
%C ..8..122...1380....20500.....260394......3602632......47228658.......627332704
%C .13..275...4800...115563....2246059.....47228658.....986337603.....20278906437
%C .21..623..16794...638791...19246379....627332704...20278906437....654433849619
%C .34.1394..58875..3550336..164006734...8353150047..420951074243..21083898963164
%C .55.3133.206084.19599537.1400773245.111159106170.8734501701701.680696834250493
%H R. H. Hardin, <a href="/A196974/b196974.txt">Table of n, a(n) for n = 1..180</a>
%e Some solutions for n=6 k=4
%e ..0..2..2..0....0..0..2..0....0..0..0..0....0..2..0..0....0..0..2..0
%e ..0..0..0..0....0..2..2..0....2..2..3..2....2..3..0..2....0..2..3..2
%e ..0..1..0..0....2..3..0..0....0..0..2..0....0..2..0..2....2..3..0..0
%e ..2..3..2..0....0..2..0..0....0..1..3..2....2..3..0..0....0..2..0..0
%e ..0..2..3..2....0..2..3..2....0..0..2..0....0..2..2..2....0..2..2..2
%e ..2..0..0..0....2..0..2..0....2..0..2..0....2..0..0..0....2..0..0..0
%Y Column 1 is A000045
%Y Column 2 is A196316
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_ Oct 08 2011