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A221999
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T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,4,6,4,1
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8
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2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 6, 10, 2, 3, 4, 6, 10, 15, 2, 3, 4, 6, 10, 15, 22, 2, 3, 4, 6, 10, 15, 22, 35, 2, 3, 4, 7, 10, 15, 22, 36, 54, 2, 3, 4, 7, 11, 15, 24, 36, 56, 81, 2, 3, 4, 7, 11, 16, 25, 39, 56, 84, 125, 2, 3, 4, 7, 11, 16, 27, 40, 60, 84, 133, 193, 2, 3, 4, 7, 11, 16, 27
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OFFSET
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1,1
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COMMENTS
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Table starts
...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2
...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3
...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4
...6...6...6...6...6...7...7...7...7...7...8...8...8...8...8...8...8...8...8
..10..10..10..10..10..11..11..11..11..11..12..12..12..12..12..12..12..12..12
..15..15..15..15..15..16..16..16..16..16..17..17..17..17..17..17..17..17..17
..22..22..22..24..25..27..27..27..27..27..29..29..29..29..29..29..29..29..29
..35..36..36..39..40..43..43..43..43..43..46..46..46..46..46..46..46..46..46
..54..56..56..60..61..65..65..67..68..68..73..73..73..73..73..73..73..73..73
..81..84..84..96.100.108.108.110.111.112.120.120.120.120.120.120.120.120.120
.125.133.135.154.160.172.172.175.176.177.189.189.190.190.190.190.190.190.191
.193.208.211.240.248.268.271.280.283.285.302.303.305.306.306.306.306.307.308
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-3) -a(n-4) -a(n-6) +a(n-7)
k=2: a(n) = a(n-1) +3*a(n-3) -2*a(n-4) -3*a(n-6) +2*a(n-7) +a(n-9)
k=3: [order 31]
k=4: [order 54]
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EXAMPLE
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Some solutions for n=7 k=4, 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....1....1....1....0....0....0....0....1....0....0....0....0....0....0
..1....1....0....0....0....1....0....0....1....0....1....0....0....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....1....0....0....0
..0....1....0....0....0....0....1....1....0....1....0....0....0....0....1....0
..0....0....0....1....0....0....0....0....0....0....1....0....0....0....0....1
..0....0....0....0....1....0....0....0....1....0....0....0....0....1....0....0
..0....1....0....0....0....1....0....1....0....0....0....0....1....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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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