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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 1,3,0,2,4 for x=0,1,2,3,4
8

%I #5 Mar 31 2012 12:36:25

%S 1,1,1,2,7,2,3,10,10,3,5,23,30,23,5,8,57,88,88,57,8,13,122,299,495,

%T 299,122,13,21,275,978,2255,2255,978,275,21,34,623,3132,10934,17093,

%U 10934,3132,623,34,55,1394,10106,54081,120633,120633,54081,10106,1394,55,89

%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 1,3,0,2,4 for x=0,1,2,3,4

%C Every 0 is next to 0 1'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 4'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.....30......88.......299.........978.........3132..........10106

%C ..3...23.....88.....495......2255.......10934........54081.........264797

%C ..5...57....299....2255.....17093......120633.......879613........6412539

%C ..8..122....978...10934....120633.....1313940.....14115912......152443404

%C .13..275...3132...54081....879613....14115912....228181579.....3665485997

%C .21..623..10106..264797...6412539...152443404...3665485997....88027683663

%C .34.1394..32721.1296124..46525107..1650437009..59089675296..2111492855742

%C .55.3133.105779.6337697.338253489.17857068383.953116106453.50695941367351

%H R. H. Hardin, <a href="/A196322/b196322.txt">Table of n, a(n) for n = 1..220</a>

%e Some solutions for n=6 k=4

%e ..0..0..0..2....0..0..0..0....0..0..0..0....2..0..0..0....0..2..0..2

%e ..0..2..2..0....0..0..2..2....2..3..2..0....0..0..0..0....2..2..0..0

%e ..0..2..3..0....0..0..2..0....0..2..2..0....2..3..2..2....0..0..0..0

%e ..0..0..2..0....2..2..3..0....0..0..0..0....0..2..0..0....2..3..2..0

%e ..0..0..2..0....0..0..2..0....2..2..2..0....2..3..0..0....0..2..2..0

%e ..0..0..2..0....0..0..2..0....0..0..2..0....0..2..0..0....2..0..0..2

%Y Column 1 is A000045

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 01 2011