A222036 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..1 array extended with zeros and convolved with -1,2,-1.

2, 4, 7, 12, 20, 33, 53, 85, 137, 221, 355, 570, 915, 1468, 2353, 3772, 6049, 9703, 15565, 24972, 40068, 64291, 103155, 165512, 265564, 426096, 683664, 1096928, 1760005, 2823900, 4530894, 7269730, 11664136, 18714867, 30027612, 48178679, 77301700

Offset

1,1

Comments

Column 1 of A222043.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - a(n-5) + a(n-6) + a(n-7) + a(n-8) - 2*a(n-9) - a(n-10) + a(n-11) + a(n-12).

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

Example

Some solutions for n=7, one extended zero followed by filtered positions:
..1....0....0....1....0....0....1....0....1....1....1....1....0....1....0....0
..0....0....0....0....0....0....0....1....0....0....0....0....1....0....1....0
..1....1....0....1....1....0....1....0....1....1....1....0....0....1....0....1
..0....0....1....0....0....0....0....1....0....0....0....1....0....0....0....0
..1....1....0....1....1....1....1....0....0....0....0....0....1....0....1....0
..0....0....0....0....0....0....0....0....0....0....0....1....0....0....0....1
..1....1....1....0....0....1....0....0....0....0....1....0....1....0....0....0
..0....0....0....0....1....0....0....0....0....1....0....1....0....0....0....1
..0....1....0....1....0....1....0....1....0....0....1....0....1....1....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A222043.

Sequence in context: A342528 A126348 A006731 * A000071 A179111 A093607

Adjacent sequences: A222033 A222034 A222035 * A222037 A222038 A222039

Keyword

nonn

Author

R. H. Hardin, Feb 06 2013

Status

approved