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A222021
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Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,3,3,1.
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1
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2, 3, 4, 6, 10, 15, 23, 36, 55, 84, 129, 198, 303, 465, 714, 1095, 1680, 2578, 3955, 6067, 9308, 14280, 21907, 33609, 51562, 79104, 121358, 186183, 285634, 438207, 672279, 1031382, 1582302, 2427501, 3724170, 5713464, 8765355, 13447438, 20630491
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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) = a(n-1) + a(n-3) + a(n-7) + a(n-9).
Empirical g.f.: x*(2 + x + x^2 + x^4 + x^5 + 2*x^6 + x^7 + x^8) / ((1 - x + x^2 - x^3 + x^4)*(1 - x^2 - x^3 - x^4 - x^5)). - Colin Barker, Aug 14 2018
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EXAMPLE
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Some solutions for n=7, one extended zero followed by filtered positions:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....0....0....0....1....0....1....0....0....0....0....1
..0....1....1....1....0....1....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....1....1....0....1....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....1....1....0....1
..0....1....0....0....0....0....0....0....0....1....0....0....0....0....0....0
..0....0....0....0....1....1....0....1....0....0....0....1....0....1....0....0
..0....0....0....1....0....0....0....0....1....0....0....0....1....0....1....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....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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