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T(n,k)=Number of nXk 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.
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%I #4 Nov 08 2016 08:38:42

%S 0,0,0,0,9,0,0,52,52,0,0,364,866,364,0,0,2523,16583,16583,2523,0,0,

%T 17424,316432,912870,316432,17424,0,0,120462,6031565,49996267,

%U 49996267,6031565,120462,0,0,832701,114975158,2732579072,7830217270,2732579072,114975158

%N T(n,k)=Number of nXk 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.

%C Table starts

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

%C .0......9.........52...........364..............2523.................17424

%C .0.....52........866.........16583............316432...............6031565

%C .0....364......16583........912870..........49996267............2732579072

%C .0...2523.....316432......49996267........7830217270.........1224179323009

%C .0..17424....6031565....2732579072.....1224179323009.......547419319384315

%C .0.120462..114975158..149393609720...191436065235070....244860735613038021

%C .0.832701.2191741025.8167589147618.29936909309888730.109526799967682916321

%H R. H. Hardin, <a href="/A278006/b278006.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=2: a(n) = 6*a(n-1) +6*a(n-2) +3*a(n-3) -6*a(n-4)

%F k=3: [order 16]

%F k=4: [order 38]

%e Some solutions for n=3 k=4

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 08 2016