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A229586
T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
14
0, 1, 0, 2, 6, 0, 6, 28, 40, 0, 16, 116, 264, 224, 0, 40, 444, 1620, 2160, 1152, 0, 96, 1620, 9156, 19764, 16416, 5632, 0, 224, 5724, 49848, 167364, 224532, 119232, 26624, 0, 512, 19764, 264300, 1375152, 2865780, 2440692, 839808, 122880, 0, 1152, 67068, 1374048
OFFSET
1,4
COMMENTS
Table starts
.0......1.......2.........6..........16...........40.............96
.0......6......28.......116.........444.........1620...........5724
.0.....40.....264......1620........9156........49848.........264300
.0....224....2160.....19764......167364......1375152.......11035044
.0...1152...16416....224532.....2865780.....35690460......435326724
.0...5632..119232...2440692....47091780....890824020....16551428868
.0..26624..839808..25745364...752194836..21639043284...613195191972
.0.122880.5785344.265720500.11768185764.515235810840.22285439501940
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1).
k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 3.
k=3: a(n) = 12*a(n-1) - 36*a(n-2).
k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 3.
k=5: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4).
k=6: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n-5) - 6561*a(n-6).
k=7: [order 8]
Empirical for row n:
n=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4.
n=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 4.
n=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 6.
n=4: [order 6] for n > 12.
n=5: [order 14] for n > 18.
n=6: [order 18] for n > 26.
n=7: [order 54] for n > 60.
EXAMPLE
Some solutions for n=3, k=4:
0 1 2 1 0 0 1 2 0 1 2 0 0 1 0 1 0 1 2 0
0 1 2 0 1 2 0 2 0 2 1 2 0 2 0 0 0 0 2 0
1 0 2 0 0 2 0 1 1 2 1 0 0 1 2 0 2 0 2 0
CROSSREFS
Row 1 is A057711(n-1).
Sequence in context: A345208 A241810 A156991 * A294789 A197035 A227805
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 26 2013
STATUS
approved