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A197889 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 0,2,1,1,1 for x=0,1,2,3,4.

%I A197889 #7 Jun 02 2025 05:13:06
%S A197889 1,0,0,1,4,1,2,3,3,2,1,14,6,14,1,1,18,47,47,18,1,3,43,77,155,77,43,3,
%T A197889 3,78,196,835,835,196,78,3,2,154,529,2263,2730,2263,529,154,2,4,305,
%U A197889 1637,10827,17890,17890,10827,1637,305,4,6,572,4235,38938,92843,129294,92843
%N A197889 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 0,2,1,1,1 for x=0,1,2,3,4.
%C A197889 Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
%C A197889 Table starts
%C A197889 .1...0.....1......2........1.........1...........3...........3...........2
%C A197889 .0...4.....3.....14.......18........43..........78.........154.........305
%C A197889 .1...3.....6.....47.......77.......196.........529........1637........4235
%C A197889 .2..14....47....155......835......2263.......10827.......38938......157178
%C A197889 .1..18....77....835.....2730.....17890.......92843......567991.....3000116
%C A197889 .1..43...196...2263....17890....129294.....1134527.....9389938....74334188
%C A197889 .3..78...529..10827....92843...1134527....13253562...145351090..1728849664
%C A197889 .3.154..1637..38938...567991...9389938...145351090..2512321052.39163260138
%C A197889 .2.305..4235.157178..3000116..74334188..1728849664.39163260138
%C A197889 .4.572.11211.654028.17111462.612587633.19259087568
%H A197889 R. H. Hardin, <a href="/A197889/b197889.txt">Table of n, a(n) for n = 1..144</a>
%e A197889 Some solutions containing all values 0 to 4 for n=6 k=4
%e A197889 ..1..2..2..1....0..2..1..0....0..1..2..0....1..2..0..1....1..2..2..1
%e A197889 ..3..1..1..0....1..1..1..2....2..1..1..1....3..1..1..2....0..1..1..0
%e A197889 ..1..4..1..2....2..1..4..1....1..4..1..2....1..4..1..2....1..4..1..2
%e A197889 ..2..1..4..1....2..1..1..3....0..1..1..2....2..1..4..1....2..1..3..1
%e A197889 ..0..1..1..3....1..0..2..1....1..2..3..1....2..1..1..3....2..1..3..1
%e A197889 ..1..2..2..1....0..1..2..1....1..2..1..0....1..0..2..1....1..0..1..2
%Y A197889 Column 1 is A017817(n+3)
%K A197889 nonn,tabl
%O A197889 1,5
%A A197889 _R. H. Hardin_ Oct 19 2011