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.

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

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 A365974

Adjacent sequences: A229682 A229683 A229684 * A229686 A229687 A229688

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 27 2013

Status

approved