A222123 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,2,1.

2, 3, 4, 8, 12, 19, 31, 48, 79, 126, 200, 322, 513, 823, 1318, 2105, 3372, 5394, 8632, 13817, 22103, 35374, 56607, 90580, 144956, 231952, 371177, 593973, 950478, 1520987, 2433908, 3894788, 6232544, 9973435, 15959719, 25539092, 40868195

Offset

1,1

Comments

Column 4 of A222127.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) + a(n-3) + 2*a(n-5) - a(n-6).

Empirical g.f.: x*(2 + x + x^2 + 2*x^3 + x^4 - x^5) / (1 - x - x^3 - 2*x^5 + x^6). - Colin Barker, Aug 15 2018

Example

Some solutions for n=7, 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....1....0....1....0....0....0....0....0....0....0....0....0....1....1
..1....1....0....0....0....1....0....1....1....0....1....0....1....0....0....0
..0....0....0....1....1....0....0....0....0....0....0....1....0....0....0....0
..0....1....1....0....0....1....0....0....0....0....0....0....1....1....0....1
..1....0....0....0....0....0....1....0....0....0....1....0....0....0....0....0
..0....0....0....0....0....0....0....1....0....0....0....1....1....1....0....0
..1....1....1....0....1....0....0....0....1....0....0....0....0....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A222127.

Sequence in context: A013914 A228718 A355958 * A222124 A222125 A222126

Adjacent sequences: A222120 A222121 A222122 * A222124 A222125 A222126

Keyword

nonn

Author

R. H. Hardin, Feb 08 2013

Status

approved