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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
0, 0, 0, 0, 2, 0, 0, 36, 36, 0, 0, 360, 888, 360, 0, 0, 2688, 10896, 10896, 2688, 0, 0, 17280, 108000, 186576, 108000, 17280, 0, 0, 101376, 959040, 2700432, 2700432, 959040, 101376, 0, 0, 559104, 7952256, 35485776, 58038768, 35485776, 7952256, 559104, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

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

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

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

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

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

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

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

EXAMPLE

Some solutions for n=3, k=4:

  0 1 2 2     0 1 2 0     0 1 1 1     0 1 1 0     0 1 1 0

  2 1 1 0     1 1 2 2     2 2 2 1     2 2 2 1     0 2 0 2

  0 0 1 0     2 0 0 0     1 1 1 0     0 0 0 2     2 1 0 1

Table starts

.0......0........0..........0............0..............0................0

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

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

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

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

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

.0.101376..7952256..437924880..21063718224...937213830720...39647663129952

.0.559104.62892288.5169543120.373936700880.25175909234736.1617006498774912

CROSSREFS

Sequence in context: A020916 A179072 A073111 * A230469 A004076 A013369

Adjacent sequences:  A229682 A229683 A229684 * A229686 A229687 A229688

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 27 2013

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)