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A229578
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T(n,k) = number of defective 4-colorings of an n X k 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
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8
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0, 1, 1, 2, 6, 2, 6, 26, 26, 6, 20, 80, 76, 80, 20, 70, 216, 171, 171, 216, 70, 246, 544, 362, 312, 362, 544, 246, 854, 1312, 757, 568, 568, 757, 1312, 854, 2920, 3072, 1584, 1064, 924, 1064, 1584, 3072, 2920, 9846, 7040, 3323, 2064, 1576, 1576, 2064, 3323, 7040
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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....20....70...246...854..2920..9846..32810.108262
....1.....6....26....80...216...544..1312..3072..7040.15872..35328..77824
....2....26....76...171...362...757..1584..3323..6982.14673..30812..64615
....6....80...171...312...568..1064..2064..4120..8384.17256..35728..74168
...20...216...362...568...924..1576..2852..5440.10780.21880..45012..93232
...70...544...757..1064..1576..2440..4048..7224.13696.27080..54928.112984
..246..1312..1584..2064..2852..4048..6108..9992.17716.33504..66188.134200
..854..3072..3323..4120..5440..7224..9992.14840.24072.42520..80296.158520
.2920..7040..6982..8384.10780.13696.17716.24072.35356.57008.100420.189400
.9846.15872.14673.17256.21880.27080.33504.42520.57008.83016.133216.234104
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4) for n > 6.
k=2: a(n) = 4*a(n-1) - 4*a(n-2) for n > 3.
k=3: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 5.
k=4: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.
k=5: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.
k=6: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.
k=7: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4) for n > 7.
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EXAMPLE
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Some solutions for n=3, k=4:
0 1 2 3 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 1
2 1 0 1 2 3 2 3 3 2 3 1 2 3 2 3 2 3 2 3
0 3 2 3 0 1 0 3 1 0 3 2 0 3 1 0 0 0 1 0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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