A229510 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

0, 0, 0, 0, 6, 0, 0, 48, 48, 0, 0, 288, 480, 288, 0, 0, 1536, 4032, 4032, 1536, 0, 0, 7680, 31104, 50112, 31104, 7680, 0, 0, 36864, 228096, 575424, 575424, 228096, 36864, 0, 0, 172032, 1617408, 6298560, 9854784, 6298560, 1617408, 172032, 0, 0, 786432

Offset

1,5

Comments

Table starts

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

.0......6.......48.......288........1536..........7680...........36864

.0.....48......480......4032.......31104........228096.........1617408

.0....288.....4032.....50112......575424.......6298560........66764736

.0...1536....31104....575424.....9854784.....162171072......2591476416

.0...7680...228096...6298560...162171072....4032737280.....97662620160

.0..36864..1617408..66764736..2591476416...97662620160...3594819388032

.0.172032.11197440.691581888.40561000128.2320483572864.130060929470976

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) - 16*a(n-2).

k=3: a(n) = 12*a(n-1) - 36*a(n-2) for n > 3.

k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 4.

k=5: [order 8] for n > 9.

k=6: [order 12] for n > 13.

k=7: [order 30] for n > 31.

Example

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

Crossrefs

Sequence in context: A019157 A019184 A019185 * A358891 A358515 A230787

Adjacent sequences: A229507 A229508 A229509 * A229511 A229512 A229513

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 25 2013

Status

approved