A229534 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.

0, 1, 0, 2, 4, 0, 6, 8, 20, 0, 16, 36, 58, 84, 0, 40, 112, 361, 356, 324, 0, 96, 368, 1588, 3064, 2038, 1188, 0, 224, 1152, 7460, 19276, 24344, 11184, 4212, 0, 512, 3568, 33136, 130854, 221096, 185808, 59626, 14580, 0, 1152, 10880, 146300, 833108, 2171944

Offset

1,4

Comments

Table starts

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

.0.....4......8.......36.......112........368.........1152..........3568

.0....20.....58......361......1588.......7460........33136........146300

.0....84....356.....3064.....19276.....130854.......833108.......5305746

.0...324...2038....24344....221096....2171944.....19965136.....184319130

.0..1188..11184...185808...2451728...34811238....463976296....6218438820

.0..4212..59626..1379512..26566266..544403948..10551803060..205336122417

.0.14580.311260.10036352.283010776.8359264560.236116939092.6668992563052

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

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) for n > 5.

k=4: a(n) = 14*a(n-1) - 57*a(n-2) + 56*a(n-3) - 16*a(n-4) for n > 5.

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

k=6: [order 18] for n > 19.

k=7: [order 38] for n > 39.

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) - 8*a(n-3) - 4*a(n-4).

n=3: a(n) = 6*a(n-1) - a(n-2) - 28*a(n-3) - 4*a(n-4) + 16*a(n-5) - 4*a(n-6) for n > 8.

n=4: [order 12] for n > 14.

n=5: [order 20] for n > 22.

n=6: [order 46] for n > 48.

n=7: [order 92] for n > 94.

Example

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

Crossrefs

Column 2 is A167682(n-1).

Row 1 is A057711(n-1).

Sequence in context: A200165 A326938 A344031 * A021810 A355007 A073800

Adjacent sequences: A229531 A229532 A229533 * A229535 A229536 A229537

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 25 2013

Status

approved