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.

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

Author

R. H. Hardin Feb 08 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..2801

Crossrefs

Column 1 is A000930(n+2)

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)