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

%I #5 Mar 31 2012 12:36:27

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,3,1,1,1,1,5,7,5,1,1,1,1,8,17,17,

%T 8,1,1,1,1,13,41,65,41,13,1,1,1,1,21,99,231,231,99,21,1,1,1,1,34,239,

%U 833,1242,833,239,34,1,1,1,1,55,577,3023,6755,6755,3023,577,55,1,1,1,1,89

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

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

%C Table starts

%C .1.1..1....1.....1.......1........1.........1...........1............1

%C .1.1..1....1.....1.......1........1.........1...........1............1

%C .1.1..2....3.....5.......8.......13........21..........34...........55

%C .1.1..3....7....17......41.......99.......239.........577.........1393

%C .1.1..5...17....65.....231......833......3023.......10988........39907

%C .1.1..8...41...231....1242.....6755.....36867......201212......1098095

%C .1.1.13...99...833....6755....55546....454787.....3731468.....30604579

%C .1.1.21..239..3023...36867...454787...5603265....69095695....851871759

%C .1.1.34..577.10988..201212..3731468..69095695..1280956817..23735291770

%C .1.1.55.1393.39907.1098095.30604579.851871759.23735291770.661075536443

%H R. H. Hardin, <a href="/A196929/b196929.txt">Table of n, a(n) for n = 1..312</a>

%e Some solutions for n=6 k=4

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

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

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

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

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

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

%Y Column 3 is A000045

%Y Column 4 is A001333(n-1)

%K nonn,tabl

%O 1,13

%A _R. H. Hardin_ Oct 07 2011