A222125 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 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, 2247, 3622, 5834, 9404, 15151, 24416, 39346, 63400, 102169, 164633, 265296, 427507, 688891, 1110104, 1788845, 2882595, 4645091, 7485216, 12061886, 19436832, 31321030, 50471539

Offset

1,1

Comments

Column 6 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) + 2*a(n-7) - a(n-8) - a(n-14) + a(n-15).

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

Crossrefs

Cf. A222127.

Sequence in context: A355958 A222123 A222124 * A222126 A004045 A060200

Adjacent sequences: A222122 A222123 A222124 * A222126 A222127 A222128

Keyword

nonn

Author

R. H. Hardin, Feb 08 2013

Status

approved