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A229580
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Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
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1
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1, 6, 40, 224, 1152, 5632, 26624, 122880, 557056, 2490368, 11010048, 48234496, 209715200, 905969664, 3892314112, 16642998272, 70866960384, 300647710720, 1271310319616, 5360119185408, 22539988369408, 94557999988736
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OFFSET
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1,2
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
Matthew Blair, Rigoberto Flórez, and Antara Mukherjee, Honeycombs in the Pascal triangle and beyond, arXiv:2203.13205 [math.HO], 2022.
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FORMULA
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Empirical: a(n) = 8*a(n-1) - 16*a(n-2) for n>3.
For n > 2: a(n) = 4*a(n-1) + 4^(n-1). - Gerald Hillier, May 01 2018
For n > 1: a(n) = (2n - 1)*2^(2n - 3), [Gerson W. Barbosa]. - Gerald Hillier, May 02 2018
Empirical g.f.: x*(1 - 2*x + 8*x^2) / (1 - 4*x)^2. - Colin Barker, May 02 2018
For n > 1: a(n) = A002064(2n-2) - A002064(2n-3). - Daniel Forgues, Aug 31 2018
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EXAMPLE
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Some solutions for n=3:
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0
0 0 2 0 0 1 0 2 1 0 2 2 1 2 2 1 0 2 1 2
1 0 0 2 1 2 1 1 2 1 1 0 0 1 0 0 0 0 0 2
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CROSSREFS
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Column 2 of A229586.
Sequence in context: A232568 A288637 A059021 * A254945 A026077 A348601
Adjacent sequences: A229577 A229578 A229579 * A229581 A229582 A229583
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KEYWORD
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nonn
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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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