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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 4,3,0,1,1 for x=0,1,2,3,4
7

%I #5 Mar 31 2012 12:36:33

%S 1,1,1,2,7,2,3,12,12,3,5,31,54,31,5,8,79,240,240,79,8,13,186,1170,

%T 2093,1170,186,13,21,465,5330,17991,17991,5330,465,21,34,1131,24689,

%U 145266,260917,145266,24689,1131,34,55,2776,116890,1255491,3964286,3964286

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

%C Table starts

%C ..1....1.......2.........3............5..............8................13

%C ..1....7......12........31...........79............186...............465

%C ..2...12......54.......240.........1170...........5330.............24689

%C ..3...31.....240......2093........17991.........145266...........1255491

%C ..5...79....1170.....17991.......260917........3964286..........61513749

%C ..8..186....5330....145266......3964286......108428600........2969407571

%C .13..465...24689...1255491.....61513749.....2969407571......147146211014

%C .21.1131..116890..10755887....932035559....81119721484.....7259079414491

%C .34.2776..549479..91079908..14154918386..2220541431613...356611993766901

%C .55.6803.2578328.776489747.215575583089.60728204921422.17542851737213231

%H R. H. Hardin, <a href="/A198155/b198155.txt">Table of n, a(n) for n = 1..144</a>

%e Some solutions containing all values 0 to 4 for n=6 k=4

%e ..1..3..1..0....0..0..0..0....1..0..0..2....1..0..0..2....0..1..3..1

%e ..0..1..0..2....2..0..0..0....3..1..2..0....3..1..2..0....1..4..1..0

%e ..1..1..3..1....1..3..1..0....1..4..1..0....1..4..1..0....3..1..2..0

%e ..3..1..1..0....1..1..4..1....1..1..3..1....0..1..3..1....1..0..0..1

%e ..1..4..1..0....3..1..1..3....3..1..2..0....0..0..0..0....0..0..1..3

%e ..0..1..3..1....1..0..0..1....1..0..0..2....2..0..0..2....2..0..0..1

%Y Column 1 is A000045

%Y Column 2 is A197229

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 21 2011