A221999 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.

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

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...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

Links

R. H. Hardin, Table of n, a(n) for n = 1..677

Formula

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]

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
..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

Crossrefs

Sequence in context: A222438 A222027 A222127 * A222334 A340716 A181948

Adjacent sequences: A221996 A221997 A221998 * A222000 A222001 A222002

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 03 2013

Status

approved