A221992 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 1,4,6,4,1.

2, 3, 4, 6, 10, 15, 22, 35, 54, 81, 125, 193, 294, 450, 692, 1060, 1622, 2488, 3815, 5843, 8955, 13729, 21038, 32239, 49415, 75734, 116062, 177879, 272623, 417812, 640332, 981380, 1504053, 2305088, 3532772, 5414309, 8297912, 12717320, 19490493

Offset

1,1

Comments

Column 1 of A221999.

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-6) + a(n-7).

Empirical g.f.: x*(1 + x + x^2)*(2 - x - x^3 + x^4) / (1 - x - 2*x^3 + x^4 + x^6 - x^7). - 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
..0....0....0....0....1....0....0....1....0....0....0....1....1....0....0....1
..0....0....1....0....0....0....1....0....0....0....1....0....0....0....0....0
..1....0....0....1....0....0....0....0....1....0....0....0....0....0....0....0
..0....0....0....0....1....1....0....0....0....1....1....0....0....0....0....1
..1....0....0....0....0....0....0....0....0....0....0....1....0....1....0....0
..0....0....0....0....0....0....0....0....1....1....0....0....1....0....1....0
..0....1....1....0....0....1....0....0....0....0....0....0....0....0....0....1
..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

Crossrefs

Cf. A221999.

Sequence in context: A147788 A104977 A206742 * A221993 A221994 A222021

Adjacent sequences: A221989 A221990 A221991 * A221993 A221994 A221995

Keyword

nonn

Author

R. H. Hardin, Feb 03 2013

Status

approved