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%I #4 Nov 23 2013 13:12:49
%S 4,4,4,8,16,8,16,20,20,16,28,72,52,72,28,52,124,176,176,124,52,96,356,
%T 484,1120,484,356,96,176,664,1500,2788,2788,1500,664,176,324,1808,
%U 4416,16884,13532,16884,4416,1808,324,596,3572,13220,44528,71888,71888,44528
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or vertically, with no adjacent elements equal
%C Table starts
%C ...4....4......8......16.......28.........52..........96..........176
%C ...4...16.....20......72......124........356.........664.........1808
%C ...8...20.....52.....176......484.......1500........4416........13220
%C ..16...72....176....1120.....2788......16884.......44528.......255432
%C ..28..124....484....2788....13532......71888......370876......1936620
%C ..52..356...1500...16884....71888.....798692.....3508240.....38129964
%C ..96..664...4416...44528...370876....3508240....31802528....296151320
%C .176.1808..13220..255432..1936620...38129964...296151320...5824262024
%C .324.3572..39524..706796.10086748..171206912..2734362948..45696457832
%C .596.9148.117892.3869856.52577472.1824149740.25388000332.894239301036
%H R. H. Hardin, <a href="/A232406/b232406.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) +a(n-3)
%F k=2: [order 9]
%F k=3: [order 12]
%F k=4: [order 29]
%F k=5: [order 56]
%e Some solutions for n=4 k=4
%e ..0..1..2..0..1....0..1..0..1..2....2..1..2..1..2....0..1..2..1..2
%e ..1..2..0..1..2....1..2..1..2..1....1..0..1..0..1....1..2..1..0..1
%e ..2..1..2..0..1....2..1..0..1..0....0..1..0..1..2....0..1..0..1..0
%e ..1..0..1..2..0....1..2..1..0..1....1..2..1..2..1....1..2..1..2..1
%e ..2..1..0..1..2....0..1..0..1..2....2..1..0..1..0....0..1..0..1..2
%Y Column 1 is 4*A000073(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 23 2013