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A258733
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Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
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1
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256, 840, 2028, 4184, 7834, 13720, 22866, 36656, 56925, 86064, 127140, 184032, 261584, 365776, 503914, 684840, 919163, 1219512, 1600812, 2080584, 2679270, 3420584, 4331890, 5444608, 6794649, 8422880, 10375620, 12705168, 15470364
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = (1/5040)*n^7 + (7/720)*n^6 + (29/144)*n^5 + (305/144)*n^4 + (1027/45)*n^3 + (16267/180)*n^2 + (2425/21)*n + 24 for n>1.
Empirical g.f.: x*(256 - 1208*x + 2476*x^2 - 2856*x^3 + 2026*x^4 - 904*x^5 + 242*x^6 - 32*x^7 + x^8) / (1 - x)^8. - Colin Barker, Jan 26 2018
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EXAMPLE
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Some solutions for n=4:
..3....0....0....2....3....1....1....1....1....0....0....0....3....2....0....0
..0....3....0....2....2....0....3....1....1....0....0....2....2....1....1....2
..0....3....2....2....2....1....2....2....1....0....0....2....2....2....1....3
..1....3....2....0....2....1....2....3....2....2....1....2....2....3....1....3
..2....1....0....1....3....1....2....3....0....2....1....3....2....3....0....3
..2....1....0....1....0....2....2....3....0....0....1....0....0....0....2....1
..2....3....2....3....1....2....0....1....1....0....3....2....3....3....3....2
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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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