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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.
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 27 2013
STATUS
approved