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A196493 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 2,3,0,1,4 for x=0,1,2,3,4.

%I A196493 #7 Jun 02 2025 04:26:23
%S A196493 1,1,1,1,1,1,1,3,3,1,1,5,9,5,1,1,9,23,23,9,1,1,17,69,99,69,17,1,1,31,
%T A196493 199,435,435,199,31,1,1,57,553,1821,2862,1821,553,57,1,1,105,1563,
%U A196493 7761,18661,18661,7761,1563,105,1,1,193,4439,33445,123151,188603,123151,33445,4439
%N A196493 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 2,3,0,1,4 for x=0,1,2,3,4.
%C A196493 Every 0 is next to 0 2's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 1's, every 4 is next to 4 4's
%C A196493 Table starts
%C A196493 .1...1.....1......1........1..........1............1.............1
%C A196493 .1...1.....3......5........9.........17...........31............57
%C A196493 .1...3.....9.....23.......69........199..........553..........1563
%C A196493 .1...5....23.....99......435.......1821.........7761.........33445
%C A196493 .1...9....69....435.....2862......18661.......123151........806609
%C A196493 .1..17...199...1821....18661.....188603......1875863......18685389
%C A196493 .1..31...553...7761...123151....1875863.....28338246.....434666223
%C A196493 .1..57..1563..33445...806609...18685389....434666223...10179007465
%C A196493 .1.105..4439.142899..5276054..187248247...6656162368..237074284215
%C A196493 .1.193.12591.610111.34627688.1876363069.101518856651.5528402854617
%H A196493 R. H. Hardin, <a href="/A196493/b196493.txt">Table of n, a(n) for n = 1..312</a>
%e A196493 Some solutions for n=6 k=4
%e A196493 ..0..0..0..1....0..1..0..0....0..0..0..0....0..0..1..0....0..1..0..0
%e A196493 ..0..1..1..3....1..3..1..0....1..3..1..0....0..0..3..1....1..3..1..0
%e A196493 ..1..3..1..1....0..0..0..0....0..1..0..0....0..0..1..0....1..0..0..0
%e A196493 ..1..3..1..0....1..3..1..1....1..0..0..0....1..3..1..0....3..1..0..1
%e A196493 ..0..1..0..0....0..1..1..3....3..1..0..0....0..1..1..0....1..0..1..3
%e A196493 ..0..0..0..0....0..0..0..1....1..0..0..0....0..1..3..1....0..0..0..1
%Y A196493 Column 2 is A000213
%K A196493 nonn,tabl
%O A196493 1,8
%A A196493 _R. H. Hardin_ Oct 03 2011