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A196477 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.

%I A196477 #7 Jun 02 2025 04:25:08
%S A196477 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 A196477 17,25,43,27,70,70,27,43,25,37,67,42,136,151,136,42,67,37,54,105,58,
%U A196477 305,557,557,305,58,105,54,79,164,94,611,2351,5955,2351,611,94,164,79,116,257
%N A196477 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 A196477 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 A196477 Table starts
%C A196477 ..1...3...4....5.....8......12.......17........25.........37..........54
%C A196477 ..3...5...8...11....18......28.......43........67........105.........164
%C A196477 ..4...8...7...14....17......27.......42........58.........94.........137
%C A196477 ..5..11..14...35....70.....136......305.......611.......1321........2832
%C A196477 ..8..18..17...70...151.....557.....2351......6926......16083.......43523
%C A196477 .12..28..27..136...557....5955....38826....128960.....351238.....1374515
%C A196477 .17..43..42..305..2351...38826...299659...1231691....5238322....26129353
%C A196477 .25..67..58..611..6926..128960..1231691...8943355...60285931...301902500
%C A196477 .37.105..94.1321.16083..351238..5238322..60285931..528624118..3818152063
%C A196477 .54.164.137.2832.43523.1374515.26129353.301902500.3818152063.48720477449
%H A196477 R. H. Hardin, <a href="/A196477/b196477.txt">Table of n, a(n) for n = 1..220</a>
%e A196477 Some solutions for n=6 k=4
%e A196477 ..0..1..1..0....1..1..0..1....1..1..0..1....1..0..0..0....1..0..0..1
%e A196477 ..0..1..1..0....0..1..1..1....0..1..1..1....1..1..1..1....1..1..1..1
%e A196477 ..0..1..1..0....0..1..1..0....0..1..1..0....0..1..4..1....0..1..1..0
%e A196477 ..1..4..1..0....1..1..1..1....1..4..1..0....0..1..1..0....0..1..1..0
%e A196477 ..1..1..1..0....1..0..0..1....1..1..1..0....1..1..1..1....1..1..1..0
%e A196477 ..0..0..1..1....1..0..0..1....0..0..1..1....1..0..0..1....1..0..1..1
%Y A196477 Column 1 is A179070(n+2)
%Y A196477 Column 2 is A196204
%Y A196477 Column 3 is A196205
%Y A196477 Column 4 is A196206
%K A196477 nonn,tabl
%O A196477 1,2
%A A196477 _R. H. Hardin_ Oct 03 2011