A231037 - OEIS

%I #4 Nov 03 2013 06:43:34

%S 0,0,0,0,0,0,0,0,2,0,0,4,10,0,0,0,0,72,32,2,0,0,32,736,1344,278,12,0,

%T 0,80,9726,17984,20250,2988,18,0,0,560,96882,677204,783848,375620,

%U 23058,56,0,0,2080,1194032,18856728,79772488,36327118,6620496,199272,170,0,0

%N T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero

%C Table starts

%C .0..0......0.........0...........0...............0...............0

%C .0..0......0.........4...........0..............32..............80

%C .0..2.....10........72.........736............9726...........96882

%C .0..0.....32......1344.......17984..........677204........18856728

%C .0..2....278.....20250......783848........79772488......5472540636

%C .0.12...2988....375620....36327118.....10140483166...1844073908022

%C .0.18..23058...6620496..1587011224...1171740348034.555813932009140

%C .0.56.199272.114765278.69795938150.139409083454936

%H R. H. Hardin, <a href="/A231037/b231037.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=2: a(n) = 2*a(n-1) +a(n-2) +4*a(n-3) -4*a(n-4)

%F k=3: [order 9]

%F k=4: [order 37]

%F Empirical for row n:

%F n=2: a(n) = 3*a(n-1) +6*a(n-2) +32*a(n-4) -20*a(n-5) +24*a(n-6) -16*a(n-7)

%F n=3: [order 33] for n>34

%e Some solutions for n=3 k=4

%e ..0..1..0..1....0..1..1..0....0..2..1..0....0..2..0..2....0..1..0..1

%e ..1..2..2..2....2..2..2..0....0..1..2..0....1..1..1..0....1..2..2..0

%e ..1..0..1..0....1..0..1..0....0..2..1..0....2..0..2..0....1..0..1..0

%Y Column 2 is A230813

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_, Nov 03 2013