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%I #7 Apr 27 2021 21:22:36
%S 0,1,0,2,6,0,6,28,40,0,16,116,264,224,0,40,444,1620,2160,1152,0,96,
%T 1620,9156,19764,16416,5632,0,224,5724,49848,167364,224532,119232,
%U 26624,0,512,19764,264300,1375152,2865780,2440692,839808,122880,0,1152,67068,1374048
%N T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally 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
%C .0......6......28.......116.........444.........1620...........5724
%C .0.....40.....264......1620........9156........49848.........264300
%C .0....224....2160.....19764......167364......1375152.......11035044
%C .0...1152...16416....224532.....2865780.....35690460......435326724
%C .0...5632..119232...2440692....47091780....890824020....16551428868
%C .0..26624..839808..25745364...752194836..21639043284...613195191972
%C .0.122880.5785344.265720500.11768185764.515235810840.22285439501940
%H R. H. Hardin, <a href="/A229586/b229586.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1).
%F k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 3.
%F k=3: a(n) = 12*a(n-1) - 36*a(n-2).
%F k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 3.
%F k=5: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).
%F k=6: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n-5) - 6561*a(n-6).
%F k=7: [order 8]
%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) = 6*a(n-1) - 9*a(n-2) for n > 4.
%F n=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 6.
%F n=4: [order 6] for n > 12.
%F n=5: [order 14] for n > 18.
%F n=6: [order 18] for n > 26.
%F n=7: [order 54] for n > 60.
%e Some solutions for n=3, k=4:
%e 0 1 2 1 0 0 1 2 0 1 2 0 0 1 0 1 0 1 2 0
%e 0 1 2 0 1 2 0 2 0 2 1 2 0 2 0 0 0 0 2 0
%e 1 0 2 0 0 2 0 1 1 2 1 0 0 1 2 0 2 0 2 0
%Y Row 1 is A057711(n-1).
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Sep 26 2013
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