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A203175
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Number of nX2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.
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4
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1, 1, 2, 4, 6, 10, 18, 30, 50, 86, 146, 246, 418, 710, 1202, 2038, 3458, 5862, 9938, 16854, 28578, 48454, 82162, 139318, 236226, 400550, 679186, 1151638, 1952738, 3311110, 5614386, 9519862, 16142082, 27370854, 46410578, 78694742, 133436450, 226257606
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OFFSET
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1,3
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COMMENTS
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It seems that for n>=1 a(n) equals the number of (n-1)-length binary words avoiding runs of zeros of length 1 (mod 3). - Milan Janjic, Feb 28 2015
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REFERENCES
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D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version. See beta_n for this sequence. - N. J. A. Sloane, Jul 08 2014
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LINKS
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FORMULA
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Empirical G.f.: -x*(1+x^2) / ( -1+x+2*x^3 ). - R. J. Mathar, Jul 02 2013
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EXAMPLE
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All solutions for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1
..1..0....1..0....1..0....1..0....1..0....1..0
..0..1....0..1....0..1....2..1....2..1....0..1
..1..0....1..2....1..0....0..1....0..2....1..2
..2..1....2..0....0..1....1..0....1..0....0..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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