A222333 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 1,1.

2, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2206, 3569, 5773, 9339, 15108, 24440, 39537, 63959, 103467, 167379, 270770, 438026, 708597, 1146301, 1854377, 2999835, 4852848, 7850477, 12699756, 20544460, 33234877, 53764229

Offset

1,1

Comments

Column 7 of A222334.

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) + a(n-7) + a(n-9) + a(n-11) + a(n-13) + a(n-15).

Empirical g.f.: x*(2 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14) / (1 - x - x^3 - x^5 - x^7 - x^9 - x^11 - x^13 - x^15). - Colin Barker, Mar 15 2018

Example

Some solutions for n=6, 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....1....0....1....0....0....0....0....0....0....0....1....1....0
..0....0....0....0....0....0....0....0....1....0....1....1....1....0....0....0
..1....0....1....1....1....0....0....0....0....0....0....0....0....0....0....1
..0....1....0....0....0....0....0....0....0....0....0....1....0....0....0....0
..1....0....0....1....0....0....0....1....0....0....0....0....1....0....1....0
..0....0....0....0....0....0....1....0....0....0....1....0....0....1....0....1

Crossrefs

Cf. A222334.

Sequence in context: A222330 A222331 A222332 * A080023 A169985 A254729

Adjacent sequences: A222330 A222331 A222332 * A222334 A222335 A222336

Keyword

nonn

Author

R. H. Hardin, Feb 15 2013

Status

approved