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.

0, 0, 0, 1, 6, 1, 3, 39, 39, 3, 12, 202, 396, 202, 12, 40, 925, 3040, 3040, 925, 40, 120, 3924, 20714, 35182, 20714, 3924, 120, 336, 15795, 131345, 362100, 362100, 131345, 15795, 336, 896, 61182, 792929, 3476928, 5655616, 3476928, 792929, 61182, 896

Offset: 1

Author

R. H. Hardin, Sep 26 2013

Keywords

• nonn
• tabl

Comments

Table starts

...0.....0.......1.........3..........12...........40............120

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

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

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

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

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

.120.15795..792929..31848813..1153135492..39229935270..1279020266434

.336.61182.4618048.281845934.15568071652.809714005005.40413033646242

Examples

			Some solutions for n=3, k=4:
  0 1 1 2     0 1 0 1     0 1 2 1     0 1 2 1     0 1 2 0
  2 0 0 1     1 2 1 2     1 2 1 1     2 0 1 2     1 0 2 1
  0 2 1 2     0 2 0 0     0 1 0 2     0 0 2 0     1 2 0 2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 1 is A052482(n-2).

Formula

Empirical for column k:

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

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

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.

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

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

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

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