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

1,5

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

Links

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

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.

Example

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

Crossrefs

Column 1 is A052482(n-2).

Sequence in context: A273081 A181552 A294347 * A101023 A195303 A354857

Adjacent sequences: A229603 A229604 A229605 * A229607 A229608 A229609

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 26 2013

Status

approved