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%I #4 Sep 22 2013 09:55:59
%S 1,2,2,4,5,4,8,13,13,8,16,34,44,34,16,32,89,153,153,89,32,64,233,536,
%T 711,536,233,64,128,610,1881,3357,3357,1881,610,128,256,1597,6604,
%U 15952,21464,15952,6604,1597,256,512,4181,23189,75965,138645,138645,75965
%N T(n,k)=Number of nXk 0..2 arrays with top left element 0, horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and antidiagonal differences never 0
%C Table starts
%C ...1....2.....4......8......16.......32.........64.........128..........256
%C ...2....5....13.....34......89......233........610........1597.........4181
%C ...4...13....44....153.....536.....1881.......6604.......23189........81428
%C ...8...34...153....711....3357....15952......75965......362012......1725628
%C ..16...89...536...3357...21464...138645.....899860.....5852687.....38099072
%C ..32..233..1881..15952..138645..1220881...10826489....96353860....859094433
%C ..64..610..6604..75965..899860.10826489..131393852..1602580515..19601243880
%C .128.1597.23189.362012.5852687.96353860.1602580515.26816872052.450388122809
%H R. H. Hardin, <a href="/A229402/b229402.txt">Table of n, a(n) for n = 1..684</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2)
%F k=3: a(n) = 5*a(n-1) -6*a(n-2) +3*a(n-3) -a(n-4)
%F k=4: [order 8]
%F k=5: [order 16]
%F k=6: [order 32]
%F k=7: [order 64]
%e Some solutions for n=4 k=4
%e ..0..2..2..1....0..2..2..1....0..2..1..0....0..2..1..1....0..2..1..0
%e ..1..0..2..2....0..0..0..2....1..0..2..1....0..2..2..1....0..2..1..1
%e ..2..1..0..0....1..1..1..0....1..0..2..2....0..0..0..2....0..0..2..2
%e ..0..2..1..1....2..2..2..1....1..1..0..2....1..1..0..0....1..0..0..2
%Y Column 1 is A000079(n-1)
%Y Column 2 is A001519(n+1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Sep 22 2013
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