A229460 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and vertically with exactly one mistake and colors introduced in row-major 0..2 order.

0, 1, 1, 2, 4, 2, 6, 20, 20, 6, 16, 84, 140, 84, 16, 40, 324, 863, 863, 324, 40, 96, 1188, 4962, 7940, 4962, 1188, 96, 224, 4212, 27313, 68790, 68790, 27313, 4212, 224, 512, 14580, 145932, 573342, 903332, 573342, 145932, 14580, 512, 1152, 49572, 763031

Offset

1,4

Comments

Table starts

...0.....1......2........6.........16..........40............96.............224

...1.....4.....20.......84........324........1188..........4212...........14580

...2....20....140......863.......4962.......27313........145932..........763031

...6....84....863.....7940......68790......573342.......4651079........36985536

..16...324...4962....68790.....903332....11451686.....141595454......1718447506

..40..1188..27313...573342...11451686...221410052....4182294415.....77626332302

..96..4212.145932..4651079..141595454..4182294415..120864516084...3435347473308

.224.14580.763031.36985536.1718447506.77626332302.3435347473308.149656305350148

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 3.

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

k=4: [order 6] for n > 7.

k=5: [order 10].

k=6: [order 14] for n > 15.

k=7: [order 26].

k=8: [order 38] for n > 39.

Example

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

Crossrefs

Column 1 is A057711(n-1).

Column 2 is A167682(n-1).

Sequence in context: A174298 A196347 A021012 * A154120 A361727 A261964

Adjacent sequences: A229457 A229458 A229459 * A229461 A229462 A229463

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 24 2013

Status

approved