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A229685 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

%I A229685 #9 Apr 28 2021 01:25:38
%S A229685 0,0,0,0,2,0,0,36,36,0,0,360,888,360,0,0,2688,10896,10896,2688,0,0,
%T A229685 17280,108000,186576,108000,17280,0,0,101376,959040,2700432,2700432,
%U A229685 959040,101376,0,0,559104,7952256,35485776,58038768,35485776,7952256,559104,0,0
%N A229685 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
%H A229685 R. H. Hardin, <a href="/A229685/b229685.txt">Table of n, a(n) for n = 1..220</a>
%F A229685 Empirical for column k:
%F A229685 k=1: a(n) = a(n-1).
%F A229685 k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 5.
%F A229685 k=3: a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3) for n > 4.
%F A229685 k=4: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 6.
%F A229685 k=5: [order 12] for n > 13.
%F A229685 k=6: [order 18] for n > 20.
%F A229685 k=7: [order 46] for n > 47.
%e A229685 Some solutions for n=3, k=4:
%e A229685   0 1 2 2     0 1 2 0     0 1 1 1     0 1 1 0     0 1 1 0
%e A229685   2 1 1 0     1 1 2 2     2 2 2 1     2 2 2 1     0 2 0 2
%e A229685   0 0 1 0     2 0 0 0     1 1 1 0     0 0 0 2     2 1 0 1
%e A229685 Table starts
%e A229685 .0......0........0..........0............0..............0................0
%e A229685 .0......2.......36........360.........2688..........17280...........101376
%e A229685 .0.....36......888......10896.......108000.........959040..........7952256
%e A229685 .0....360....10896.....186576......2700432.......35485776........437924880
%e A229685 .0...2688...108000....2700432.....58038768.....1138164048......21063718224
%e A229685 .0..17280...959040...35485776...1138164048....33555543408.....937213830720
%e A229685 .0.101376..7952256..437924880..21063718224...937213830720...39647663129952
%e A229685 .0.559104.62892288.5169543120.373936700880.25175909234736.1617006498774912
%K A229685 nonn,tabl
%O A229685 1,5
%A A229685 _R. H. Hardin_, Sep 27 2013