A222121 Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,2,1.

2, 3, 4, 6, 10, 15, 24, 38, 59, 92, 144, 224, 350, 547, 854, 1334, 2084, 3254, 5082, 7937, 12395, 19358, 30233, 47216, 73740, 115164, 179857, 280892, 438684, 685115, 1069980, 1671044, 2609756, 4075792, 6365377, 9941140, 15525596, 24247132

Offset

1,1

Comments

Column 2 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-6) + a(n-8).

Empirical g.f.: x*(2 + x + x^2 + x^4 + x^5 + x^6 + x^7) / ((1 + x + x^2)*(1 - 2*x + x^2 - x^4 + x^5 - x^6)). - 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....0....0....0....1....1....0....0....0....1....0....0....1....0
..0....0....0....0....0....0....0....0....1....1....0....0....1....1....0....1
..0....0....1....1....0....1....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....0....1....0....1....0....0....1....0....0....0....0
..1....1....1....0....0....0....0....0....0....1....0....0....0....0....0....0
..0....0....0....0....1....1....1....1....0....0....0....0....0....0....0....1
..0....0....0....1....0....0....0....0....0....0....0....1....0....1....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A222127.

Sequence in context: A222021 A186426 A018062 * A221995 A364587 A221996

Adjacent sequences: A222118 A222119 A222120 * A222122 A222123 A222124

Keyword

nonn

Author

R. H. Hardin, Feb 08 2013

Status

approved