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A222127
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 1,2,1
7
2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 6, 9, 2, 3, 4, 7, 10, 13, 2, 3, 4, 8, 11, 15, 19, 2, 3, 4, 8, 12, 17, 24, 28, 2, 3, 4, 8, 12, 19, 27, 38, 41, 2, 3, 4, 8, 12, 19, 31, 42, 59, 60, 2, 3, 4, 8, 12, 19, 31, 48, 66, 92, 88, 2, 3, 4, 8, 12, 19, 31, 48, 79, 104, 144, 129, 2, 3, 4, 8, 12, 20, 31, 49
OFFSET
1,1
COMMENTS
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...7...8...8...8...8...8...8...8...8...8...8...8...8...8...8...8...8
...9..10..11..12..12..12..12..12..12..12..12..12..12..12..12..12..12..12..12
..13..15..17..19..19..19..19..20..21..21..21..21..21..21..21..21..21..21..21
..19..24..27..31..31..31..31..32..33..33..33..33..33..33..33..33..33..33..33
..28..38..42..48..48..49..49..51..53..53..53..53..53..53..54..55..55..55..55
..41..59..66..79..79..80..80..83..86..86..86..86..86..86..87..88..88..88..88
..60..92.104.126.126.128.128.132.136.137.138.138.138.138.140.142.142.142.142
..88.144.163.200.201.207.207.215.224.224.224.224.224.224.227.230.230.230.230
.129.224.256.322.323.334.334.346.360.360.360.360.360.360.365.369.370.371.371
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-3)
k=2: a(n) = a(n-1) +a(n-3) +a(n-6) +a(n-8)
k=3: a(n) = a(n-1) +a(n-3) +a(n-5)
k=4: a(n) = a(n-1) +a(n-3) +2*a(n-5) -a(n-6)
k=5: a(n) = a(n-1) +a(n-3) +a(n-5) +a(n-8) +a(n-10) +2*a(n-12) -a(n-13)
k=6: a(n) = a(n-1) +a(n-3) +a(n-5) +2*a(n-7) -a(n-8) -a(n-14) +a(n-15)
k=7: a(n) = a(n-1) +a(n-3) +a(n-5) +3*a(n-7) -2*a(n-8) -a(n-10) -a(n-12) -2*a(n-14) +a(n-15)
EXAMPLE
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
..1....0....1....0....1....0....0....0....1....0....1....0....0....0....0....0
..0....1....0....0....0....1....0....0....0....0....0....1....0....0....1....1
..0....0....1....0....0....0....1....1....1....0....0....0....0....0....0....0
..1....0....0....0....0....0....0....0....0....1....0....1....0....0....0....1
..0....1....0....0....0....1....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....1....0....0....1....0....0....1....0....0....0
..1....0....1....1....0....1....0....1....0....0....1....0....0....0....1....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
CROSSREFS
Column 1 is A000930(n+2)
Sequence in context: A222111 A222438 A222027 * A221999 A222334 A340716
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Feb 08 2013
STATUS
approved