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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. 8

%I #9 Apr 28 2021 01:25:38

%S 0,0,0,0,2,0,0,36,36,0,0,360,888,360,0,0,2688,10896,10896,2688,0,0,

%T 17280,108000,186576,108000,17280,0,0,101376,959040,2700432,2700432,

%U 959040,101376,0,0,559104,7952256,35485776,58038768,35485776,7952256,559104,0,0

%N 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 R. H. Hardin, <a href="/A229685/b229685.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1).

%F k=2: a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n > 5.

%F k=3: a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3) for n > 4.

%F k=4: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 6.

%F k=5: [order 12] for n > 13.

%F k=6: [order 18] for n > 20.

%F k=7: [order 46] for n > 47.

%e Some solutions for n=3, k=4:

%e 0 1 2 2 0 1 2 0 0 1 1 1 0 1 1 0 0 1 1 0

%e 2 1 1 0 1 1 2 2 2 2 2 1 2 2 2 1 0 2 0 2

%e 0 0 1 0 2 0 0 0 1 1 1 0 0 0 0 2 2 1 0 1

%e Table starts

%e .0......0........0..........0............0..............0................0

%e .0......2.......36........360.........2688..........17280...........101376

%e .0.....36......888......10896.......108000.........959040..........7952256

%e .0....360....10896.....186576......2700432.......35485776........437924880

%e .0...2688...108000....2700432.....58038768.....1138164048......21063718224

%e .0..17280...959040...35485776...1138164048....33555543408.....937213830720

%e .0.101376..7952256..437924880..21063718224...937213830720...39647663129952

%e .0.559104.62892288.5169543120.373936700880.25175909234736.1617006498774912

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Sep 27 2013

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