%I #4 Dec 02 2013 18:18:02

%S 3,6,6,12,12,12,24,26,26,24,48,56,84,56,48,96,120,252,252,120,96,192,

%T 258,774,1048,774,258,192,384,554,2360,4458,4458,2360,554,384,768,

%U 1190,7212,18850,26644,18850,7212,1190,768,1536,2556,22024,79810,157322,157322

%N T(n,k)=Number of nXk 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally

%C Table starts

%C ....3....6.....12......24........48.........96..........192...........384

%C ....6...12.....26......56.......120........258..........554..........1190

%C ...12...26.....84.....252.......774.......2360.........7212.........22024

%C ...24...56....252....1048......4458......18850........79810........337850

%C ...48..120....774....4458.....26644.....157322.......932576.......5521380

%C ...96..258...2360...18850....157322....1294504.....10700160......88318190

%C ..192..554...7212...79810....932576...10700160....123516664....1422959686

%C ..384.1190..22024..337850...5521380...88318190...1422959686...22870954236

%C ..768.2556..67272.1430144..32701386..729295244..16403819514..367894792064

%C .1536.5490.205466.6054098.193661452.6021446660.189062126148.5916284262276

%H R. H. Hardin, <a href="/A232941/b232941.txt">Table of n, a(n) for n = 1..924</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) -a(n-5) for n>6

%F k=4: [order 8] for n>9

%F k=5: [order 13] for n>14

%F k=6: [order 21] for n>22

%F k=7: [order 34] for n>35

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A003945

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 02 2013