A229637 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.

0, 0, 0, 1, 6, 0, 3, 40, 39, 0, 12, 122, 244, 202, 0, 40, 488, 1109, 1496, 925, 0, 120, 1608, 6031, 10227, 8800, 3924, 0, 336, 5392, 28448, 77620, 89331, 50084, 15795, 0, 896, 17368, 136778, 535671, 960325, 747299, 277996, 61182, 0, 2304, 55232, 633328

Offset: 1

Author

R. H. Hardin, Sep 27 2013

Keywords

• nonn
• tabl

Comments

Table starts

.0.....0.......1........3.........12..........40...........120............336

.0.....6......40......122........488........1608..........5392..........17368

.0....39.....244.....1109.......6031.......28448........136778.........633328

.0...202....1496....10227......77620......535671.......3723370.......25022190

.0...925....8800....89331.....960325.....9722206......98015235......960209886

.0..3924...50084...747299...11485716...170405645....2495874984....35693194243

.0.15795..277996..6049298..133784624..2902520386...61836040854..1290897457785

.0.61182.1513104.47723226.1525870912.48303362606.1498317588826.45634751291449

Examples

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

Links

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

Crossrefs

Column 2 is A229600.

Row 1 is A052482(n-2).

Formula

Empirical for column k:

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

k=2: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n > 5

k=3: a(n) = 15*a(n-1) - 81*a(n-2) + 185*a(n-3) - 162*a(n-4) + 60*a(n-5) - 8*a(n-6) for n > 7.

k=4: [order 6] for n > 9.

k=5: [order 18] for n > 20.

k=6: [order 27] for n > 30.

k=7: [order 57] for n > 60.

Empirical for row n:

n=1: a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 6.

n=2: a(n) = 6*a(n-1) - 6*a(n-2) - 16*a(n-3) + 12*a(n-4) + 24*a(n-5) + 8*a(n-6).

n=3: [order 9] for n > 12.

n=4: [order 18] for n > 21.

n=5: [order 30] for n > 33.

n=6: [order 69] for n > 72.