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

Author

R. H. Hardin, Sep 25 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A167682(n-1).

Row 1 is A057711(n-1).

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.