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A222123
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Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,2,1.
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1
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2, 3, 4, 8, 12, 19, 31, 48, 79, 126, 200, 322, 513, 823, 1318, 2105, 3372, 5394, 8632, 13817, 22103, 35374, 56607, 90580, 144956, 231952, 371177, 593973, 950478, 1520987, 2433908, 3894788, 6232544, 9973435, 15959719, 25539092, 40868195
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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) + 2*a(n-5) - a(n-6).
Empirical g.f.: x*(2 + x + x^2 + 2*x^3 + x^4 - x^5) / (1 - x - x^3 - 2*x^5 + x^6). - Colin Barker, Aug 15 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....1....0....1....0....0....0....0....0....0....0....0....0....1....1
..1....1....0....0....0....1....0....1....1....0....1....0....1....0....0....0
..0....0....0....1....1....0....0....0....0....0....0....1....0....0....0....0
..0....1....1....0....0....1....0....0....0....0....0....0....1....1....0....1
..1....0....0....0....0....0....1....0....0....0....1....0....0....0....0....0
..0....0....0....0....0....0....0....1....0....0....0....1....1....1....0....0
..1....1....1....0....1....0....0....0....1....0....0....0....0....0....1....0
..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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