A229586 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

0, 1, 0, 2, 6, 0, 6, 28, 40, 0, 16, 116, 264, 224, 0, 40, 444, 1620, 2160, 1152, 0, 96, 1620, 9156, 19764, 16416, 5632, 0, 224, 5724, 49848, 167364, 224532, 119232, 26624, 0, 512, 19764, 264300, 1375152, 2865780, 2440692, 839808, 122880, 0, 1152, 67068, 1374048

Offset

1,4

Comments

Table starts

.0......1.......2.........6..........16...........40.............96

.0......6......28.......116.........444.........1620...........5724

.0.....40.....264......1620........9156........49848.........264300

.0....224....2160.....19764......167364......1375152.......11035044

.0...1152...16416....224532.....2865780.....35690460......435326724

.0...5632..119232...2440692....47091780....890824020....16551428868

.0..26624..839808..25745364...752194836..21639043284...613195191972

.0.122880.5785344.265720500.11768185764.515235810840.22285439501940

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 3.

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

k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 3.

k=5: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).

k=6: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n-5) - 6561*a(n-6).

k=7: [order 8]

Empirical for row n:

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

n=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 4.

n=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 6.

n=4: [order 6] for n > 12.

n=5: [order 14] for n > 18.

n=6: [order 18] for n > 26.

n=7: [order 54] for n > 60.

Example

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

Crossrefs

Row 1 is A057711(n-1).

Sequence in context: A345208 A241810 A156991 * A294789 A197035 A227805

Adjacent sequences: A229583 A229584 A229585 * A229587 A229588 A229589

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 26 2013

Status

approved