A222126 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..7 array extended with zeros and convolved with 1,2,1.

2, 3, 4, 8, 12, 19, 31, 49, 80, 128, 207, 334, 536, 866, 1394, 2248, 3624, 5839, 9414, 15169, 24452, 39411, 63521, 102387, 165020, 265982, 428703, 690979, 1113717, 1795071, 2893285, 4663357, 7516351, 12114776, 19526459, 31472549, 50727107

Offset

1,1

Comments

Column 7 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) + a(n-5) + 3*a(n-7) - 2*a(n-8) - a(n-10) - a(n-12) - 2*a(n-14) + a(n-15).

Empirical g.f.: x*(2 + x + x^2 + 2*x^3 + x^4 + x^5 + x^6 - 4*x^7 - x^8 - x^9 - 3*x^10 - x^11 - 2*x^12 - x^13 + x^14) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)*(1 - x - x^3 - x^5 - 2*x^7 + x^8)). - 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
..1....0....0....0....0....0....0....0....1....1....0....0....1....0....0....0
..0....0....1....0....1....0....1....0....0....0....1....0....0....1....0....0
..0....0....0....0....0....1....0....1....0....1....0....0....0....0....0....0
..0....1....0....0....0....0....0....0....1....0....0....1....1....1....1....0
..0....0....0....1....0....0....0....1....0....0....1....0....0....0....0....0
..1....0....1....0....0....1....0....0....0....0....0....0....0....0....1....1
..0....0....0....0....1....0....0....0....0....1....0....1....1....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A222127.

Sequence in context: A222123 A222124 A222125 * A004045 A060200 A057608

Adjacent sequences: A222123 A222124 A222125 * A222127 A222128 A222129

Keyword

nonn

Author

R. H. Hardin, Feb 08 2013

Status

approved