A222022 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..3 array extended with zeros and convolved with 1,3,3,1.

2, 3, 4, 7, 11, 16, 26, 41, 62, 99, 156, 242, 382, 600, 938, 1475, 2314, 3627, 5696, 8935, 14016, 22000, 34515, 54153, 84981, 133334, 209209, 328278, 515083, 808208, 1268156, 1989823, 3122203, 4899001, 7686907, 12061403, 18925330, 29695352

Offset

1,1

Comments

Column 3 of A222027.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-3) - a(n-4) + a(n-8) - a(n-9) + a(n-11) - a(n-12) - 2*a(n-14) + a(n-15).

Empirical g.f.: x*(2 + x + x^2 - x^3 - 2*x^8 - 2*x^11 - x^12 - x^13 + x^14) / ((1 - x)*(1 + x + x^2)*(1 - x - x^3 - x^6 - x^8 - 2*x^11 + x^12)). - Colin Barker, Aug 14 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....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....0....1....1....0....1....0....1....0....1....0....0....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....1....1....0
..0....1....0....0....1....0....1....0....0....0....0....1....0....0....0....1
..0....0....1....1....0....1....0....0....0....0....1....0....0....1....0....0
..1....0....0....0....1....0....0....1....0....0....0....0....0....0....0....0
..0....0....1....0....0....1....1....0....0....0....0....0....1....0....0....0
..0....1....0....0....0....0....0....0....0....0....1....1....0....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A222027.

Sequence in context: A210518 A113435 A367667 * A025048 A017987 A337495

Adjacent sequences: A222019 A222020 A222021 * A222023 A222024 A222025

Keyword

nonn

Author

R. H. Hardin, Feb 05 2013

Status

approved