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%I #8 Apr 27 2021 20:53:06
%S 0,1,1,2,4,2,6,20,20,6,16,84,140,84,16,40,324,863,863,324,40,96,1188,
%T 4962,7940,4962,1188,96,224,4212,27313,68790,68790,27313,4212,224,512,
%U 14580,145932,573342,903332,573342,145932,14580,512,1152,49572,763031
%N T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly one mistake and colors introduced in row-major 0..2 order.
%C Table starts
%C ...0.....1......2........6.........16..........40............96.............224
%C ...1.....4.....20.......84........324........1188..........4212...........14580
%C ...2....20....140......863.......4962.......27313........145932..........763031
%C ...6....84....863.....7940......68790......573342.......4651079........36985536
%C ..16...324...4962....68790.....903332....11451686.....141595454......1718447506
%C ..40..1188..27313...573342...11451686...221410052....4182294415.....77626332302
%C ..96..4212.145932..4651079..141595454..4182294415..120864516084...3435347473308
%C .224.14580.763031.36985536.1718447506.77626332302.3435347473308.149656305350148
%H R. H. Hardin, <a href="/A229460/b229460.txt">Table of n, a(n) for n = 1..420</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4.
%F k=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 3.
%F k=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).
%F k=4: [order 6] for n > 7.
%F k=5: [order 10].
%F k=6: [order 14] for n > 15.
%F k=7: [order 26].
%F k=8: [order 38] for n > 39.
%e Some solutions for n=3, k=4:
%e 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 2
%e 2 1 2 1 2 1 2 0 2 2 1 0 1 0 2 1 1 0 2 0
%e 0 2 1 2 1 2 1 2 0 1 2 1 2 0 1 0 1 2 0 2
%Y Column 1 is A057711(n-1).
%Y Column 2 is A167682(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Sep 24 2013