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%I #9 Apr 27 2021 21:24:32
%S 0,1,0,2,4,0,6,8,20,0,16,36,58,84,0,40,112,361,356,324,0,96,368,1588,
%T 3064,2038,1188,0,224,1152,7460,19276,24344,11184,4212,0,512,3568,
%U 33136,130854,221096,185808,59626,14580,0,1152,10880,146300,833108,2171944
%N T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally 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 .0.....4......8.......36.......112........368.........1152..........3568
%C .0....20.....58......361......1588.......7460........33136........146300
%C .0....84....356.....3064.....19276.....130854.......833108.......5305746
%C .0...324...2038....24344....221096....2171944.....19965136.....184319130
%C .0..1188..11184...185808...2451728...34811238....463976296....6218438820
%C .0..4212..59626..1379512..26566266..544403948..10551803060..205336122417
%C .0.14580.311260.10036352.283010776.8359264560.236116939092.6668992563052
%H R. H. Hardin, <a href="/A229534/b229534.txt">Table of n, a(n) for n = 1..337</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1).
%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) for n > 5.
%F k=4: a(n) = 14*a(n-1) - 57*a(n-2) + 56*a(n-3) - 16*a(n-4) for n > 5.
%F k=5: [order 12] for n > 13.
%F k=6: [order 18] for n > 19.
%F k=7: [order 38] for n > 39.
%F Empirical for row n:
%F n=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4.
%F n=2: a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4).
%F n=3: a(n) = 6*a(n-1) - a(n-2) - 28*a(n-3) - 4*a(n-4) + 16*a(n-5) - 4*a(n-6) for n > 8.
%F n=4: [order 12] for n > 14.
%F n=5: [order 20] for n > 22.
%F n=6: [order 46] for n > 48.
%F n=7: [order 92] for n > 94.
%e Some solutions for n=3, k=4:
%e 0 1 0 1 0 1 0 2 0 1 0 0 0 1 0 0 0 1 2 0
%e 0 2 0 2 1 2 0 2 0 1 2 1 2 1 2 1 0 1 2 0
%e 2 1 0 1 1 2 0 2 2 1 2 1 0 1 2 1 2 1 0 1
%Y Column 2 is A167682(n-1).
%Y Row 1 is A057711(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Sep 25 2013
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