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A255995
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Number of length n+4 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
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1
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32, 64, 100, 144, 196, 257, 328, 410, 504, 611, 732, 868, 1020, 1189, 1376, 1582, 1808, 2055, 2324, 2616, 2932, 3273, 3640, 4034, 4456, 4907, 5388, 5900, 6444, 7021, 7632, 8278, 8960, 9679, 10436, 11232, 12068, 12945, 13864, 14826, 15832, 16883, 17980
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/6)*n^3 + 2*n^2 + (143/6)*n + 6 for n>2.
Empirical g.f.: x*(32 - 64*x + 36*x^2 - 4*x^4 + x^5) / (1 - x)^4. - Colin Barker, Jan 25 2018
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EXAMPLE
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Some solutions for n=4:
..0....1....1....1....0....1....1....1....0....1....1....0....0....1....0....0
..0....1....0....1....1....1....0....0....1....0....0....0....0....0....0....1
..0....1....0....0....0....0....0....0....1....0....0....0....0....1....1....0
..0....0....0....0....0....1....1....0....1....1....0....1....0....1....0....0
..0....0....0....1....1....1....1....0....0....1....1....1....0....1....0....1
..0....0....0....1....1....1....1....0....0....1....0....0....1....1....0....1
..0....0....0....0....0....1....0....0....0....1....1....0....0....1....0....1
..1....1....0....0....1....1....0....1....1....1....1....0....0....1....1....0
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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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