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

%I #5 Mar 31 2012 12:36:26

%S 1,1,1,2,7,2,3,20,20,3,5,65,120,65,5,8,203,698,698,203,8,13,648,4078,

%T 7407,4078,648,13,21,2057,24032,79091,79091,24032,2057,21,34,6527,

%U 141460,839370,1522940,839370,141460,6527,34,55,20740,830652,8980645,29573040

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

%C Every 0 is next to 0 3's, every 1 is next to 1 2's, every 2 is next to 2 0's, every 3 is next to 3 1's, every 4 is next to 4 4's

%C Table starts

%C ..1.....1........2...........3.............5................8

%C ..1.....7.......20..........65...........203..............648

%C ..2....20......120.........698..........4078............24032

%C ..3....65......698........7407.........79091...........839370

%C ..5...203.....4078.......79091.......1522940.........29573040

%C ..8...648....24032......839370......29573040.......1051645368

%C .13..2057...141460.....8980645.....578185580......37529013812

%C .21..6527...830652....96049685...11258527547....1334022464052

%C .34.20740..4886324..1025896374..219297645143...47492318713306

%C .55.65833.28734972.10959530915.4274120207800.1690727011393186

%H R. H. Hardin, <a href="/A196590/b196590.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions for n=6 k=4

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

%e ..0..0..0..0....0..1..2..0....0..2..2..2....0..0..0..0....0..0..1..0

%e ..0..1..1..2....0..1..1..1....2..2..0..0....0..0..1..2....1..1..2..0

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

%e ..0..0..0..2....0..1..0..0....0..0..0..0....1..0..1..0....0..0..0..0

%e ..0..2..1..1....0..0..2..1....0..0..0..2....0..0..2..0....2..0..2..1

%Y Column 1 is A000045

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 04 2011