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A229586
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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.
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14
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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
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..287
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FORMULA
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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.
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EXAMPLE
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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
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CROSSREFS
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Row 1 is A057711(n-1).
Sequence in context: A345208 A241810 A156991 * A294789 A197035 A227805
Adjacent sequences: A229583 A229584 A229585 * A229587 A229588 A229589
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Sep 26 2013
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STATUS
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approved
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