login
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 4,0,3,2,1 for x=0,1,2,3,4
5

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

%S 1,3,3,4,5,4,5,8,8,5,8,11,7,11,8,12,18,14,14,18,12,17,28,17,35,17,28,

%T 17,25,43,27,70,70,27,43,25,37,67,42,136,151,136,42,67,37,54,105,58,

%U 305,557,557,305,58,105,54,79,164,94,611,2351,5955,2351,611,94,164,79,116,257

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

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

%C Table starts

%C ..1...3...4....5.....8......12.......17........25.........37..........54

%C ..3...5...8...11....18......28.......43........67........105.........164

%C ..4...8...7...14....17......27.......42........58.........94.........137

%C ..5..11..14...35....70.....136......305.......611.......1321........2832

%C ..8..18..17...70...151.....557.....2351......6926......16083.......43523

%C .12..28..27..136...557....5955....38826....128960.....351238.....1374515

%C .17..43..42..305..2351...38826...299659...1231691....5238322....26129353

%C .25..67..58..611..6926..128960..1231691...8943355...60285931...301902500

%C .37.105..94.1321.16083..351238..5238322..60285931..528624118..3818152063

%C .54.164.137.2832.43523.1374515.26129353.301902500.3818152063.48720477449

%H R. H. Hardin, <a href="/A196477/b196477.txt">Table of n, a(n) for n = 1..220</a>

%e Some solutions for n=6 k=4

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

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

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

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

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

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

%Y Column 1 is A179070(n+2)

%Y Column 2 is A196204

%Y Column 3 is A196205

%Y Column 4 is A196206

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Oct 03 2011