A222127 - OEIS

%I #4 Feb 08 2013 08:11:10

%S 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,

%T 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,

%U 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

%N 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

%C Table starts

%C ...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2...2

%C ...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3...3

%C ...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4...4

%C ...6...6...7...8...8...8...8...8...8...8...8...8...8...8...8...8...8...8...8

%C ...9..10..11..12..12..12..12..12..12..12..12..12..12..12..12..12..12..12..12

%C ..13..15..17..19..19..19..19..20..21..21..21..21..21..21..21..21..21..21..21

%C ..19..24..27..31..31..31..31..32..33..33..33..33..33..33..33..33..33..33..33

%C ..28..38..42..48..48..49..49..51..53..53..53..53..53..53..54..55..55..55..55

%C ..41..59..66..79..79..80..80..83..86..86..86..86..86..86..87..88..88..88..88

%C ..60..92.104.126.126.128.128.132.136.137.138.138.138.138.140.142.142.142.142

%C ..88.144.163.200.201.207.207.215.224.224.224.224.224.224.227.230.230.230.230

%C .129.224.256.322.323.334.334.346.360.360.360.360.360.360.365.369.370.371.371

%H R. H. Hardin, <a href="/A222127/b222127.txt">Table of n, a(n) for n = 1..2801</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-3)

%F k=2: a(n) = a(n-1) +a(n-3) +a(n-6) +a(n-8)

%F k=3: a(n) = a(n-1) +a(n-3) +a(n-5)

%F k=4: a(n) = a(n-1) +a(n-3) +2*a(n-5) -a(n-6)

%F 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)

%F 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)

%F 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)

%e Some solutions for n=7 k=4, one extended zero followed by filtered positions

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....0....1....0....1....0....0....0....1....0....1....0....0....0....0....0

%e ..0....1....0....0....0....1....0....0....0....0....0....1....0....0....1....1

%e ..0....0....1....0....0....0....1....1....1....0....0....0....0....0....0....0

%e ..1....0....0....0....0....0....0....0....0....1....0....1....0....0....0....1

%e ..0....1....0....0....0....1....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....0....0....0....1....0....0....1....0....0....1....0....0....0

%e ..1....0....1....1....0....1....0....1....0....0....1....0....0....0....1....1

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%Y Column 1 is A000930(n+2)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Feb 08 2013