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%I #4 Nov 17 2013 13:58:13
%S 1,2,2,4,6,4,6,14,14,6,10,30,46,30,10,16,66,130,130,66,16,26,146,410,
%T 534,410,146,26,42,322,1194,2230,2230,1194,322,42,68,710,3722,9310,
%U 13538,9310,3722,710,68,110,1566,10942,38870,75462,75462,38870,10942,1566,110
%N T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal
%C Table starts
%C ...1....2......4.......6.......10.........16..........26............42
%C ...2....6.....14......30.......66........146.........322...........710
%C ...4...14.....46.....130......410.......1194........3722.........10942
%C ...6...30....130.....534.....2230.......9310.......38870........162278
%C ..10...66....410....2230....13538......75462......457234.......2561258
%C ..16..146...1194....9310....75462.....612364.....4990482......40661766
%C ..26..322...3722...38870...457234....4990482....59448262.....653375842
%C ..42..710..10942..162278..2561258...40661766...653375842...10508498862
%C ..68.1566..33806..677510.15454594..331554282..7789998594..169516703810
%C .110.3454.100142.2828606.86936482.2703411654.85859588738.2735194512174
%H R. H. Hardin, <a href="/A232065/b232065.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2) for n>3
%F k=2: a(n) = 2*a(n-1) +a(n-3)
%F k=3: a(n) = a(n-1) +7*a(n-2) -3*a(n-3) +3*a(n-4) -7*a(n-5) +2*a(n-6) -2*a(n-7) +2*a(n-8)
%F k=4: a(n) = 4*a(n-1) +a(n-2) -4*a(n-4) -3*a(n-5) +a(n-7) +3*a(n-8) -a(n-11)
%F k=5: [order 20] for n>22
%F k=6: [order 42]
%e Some solutions for n=5 k=4
%e ..2..1..0..1....2..1..2..1....2..0..1..0....2..1..2..1....1..2..1..2
%e ..1..0..1..2....1..2..1..2....0..1..2..1....1..0..1..2....0..1..0..1
%e ..0..1..0..1....2..1..2..1....1..0..1..2....0..1..2..1....1..0..1..2
%e ..1..2..1..2....1..0..1..0....2..1..2..1....1..0..1..2....2..1..2..1
%e ..2..1..2..1....2..1..2..1....1..0..1..0....2..1..2..1....1..0..1..0
%Y Column 1 is A006355(n+1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 17 2013
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