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

%I #5 Mar 31 2012 12:36:29

%S 1,1,1,2,7,2,3,10,10,3,5,23,31,23,5,8,57,98,98,57,8,13,122,344,639,

%T 344,122,13,21,275,1139,3181,3181,1139,275,21,34,623,3750,15930,27709,

%U 15930,3750,623,34,55,1394,12470,85087,207538,207538,85087,12470,1394,55,89

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

%C Every 0 is next to 0 4's, every 1 is next to 1 4'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.....31.......98.......344........1139..........3750...........12470

%C ..3...23.....98......639......3181.......15930.........85087..........450159

%C ..5...57....344.....3181.....27709......207538.......1711736........14233577

%C ..8..122...1139....15930....207538.....2533633......32070816.......406507906

%C .13..275...3750....85087...1711736....32070816.....638181656.....12585831905

%C .21..623..12470...450159..14233577...406507906...12585831905....388800452625

%C .34.1394..41479..2373372.115744195..5121683931..246443960437..11842674409406

%C .55.3133.137872.12475923.943877937.64661725576.4851375382650.362552810954997

%H R. H. Hardin, <a href="/A197307/b197307.txt">Table of n, a(n) for n = 1..180</a>

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

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

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

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

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

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

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

%Y Column 1 is A000045

%Y Column 2 is A196316

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 13 2011