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A229606 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order. 8

%I

%S 0,0,0,1,6,1,3,39,39,3,12,202,396,202,12,40,925,3040,3040,925,40,120,

%T 3924,20714,35182,20714,3924,120,336,15795,131345,362100,362100,

%U 131345,15795,336,896,61182,792929,3476928,5655616,3476928,792929,61182,896

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

%C Table starts

%C ...0.....0.......1.........3..........12...........40............120

%C ...0.....6......39.......202.........925.........3924..........15795

%C ...1....39.....396......3040.......20714.......131345.........792929

%C ...3...202....3040.....35182......362100......3476928.......31848813

%C ..12...925...20714....362100.....5655616.....82613904.....1153135492

%C ..40..3924..131345...3476928....82613904...1840258874....39229935270

%C .120.15795..792929..31848813..1153135492..39229935270..1279020266434

%C .336.61182.4618048.281845934.15568071652.809714005005.40413033646242

%H R. H. Hardin, <a href="/A229606/b229606.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F k=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.

%F k=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 5.

%F k=3: a(n) = 15*a(n-1) - 81*a(n-2) + 185*a(n-3) - 162*a(n-4) + 60*a(n-5) - 8*a(n-6) for n > 7.

%F k=4: [order 9] for n > 11.

%F k=5: [order 16] for n > 17.

%F k=6: [order 21] for n > 23.

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

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

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

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

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

%Y Column 1 is A052482(n-2).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Sep 26 2013

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)