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

1,5

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

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) = 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.

Example

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

Crossrefs

Column 2 is A229600.

Row 1 is A052482(n-2).

Sequence in context: A173685 A019108 A019115 * A019109 A089841 A202542

Adjacent sequences: A229634 A229635 A229636 * A229638 A229639 A229640

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 27 2013

Status

approved