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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
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 (list; table; graph; refs; listen; history; text; internal format)
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 A160199

Adjacent sequences:  A229603 A229604 A229605 * A229607 A229608 A229609

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 26 2013

STATUS

approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)