A222431 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 1,1,1.

2, 3, 4, 5, 8, 12, 18, 26, 40, 60, 90, 134, 202, 303, 454, 680, 1021, 1532, 2298, 3447, 5173, 7762, 11646, 17473, 26218, 39338, 59023, 88558, 132875, 199368, 299135, 448827, 673430, 1010428, 1516066, 2274735, 3413059, 5121022, 7683683, 11528750

Offset

1,1

Comments

Column 1 of A222438.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - 3*a(n-5) + a(n-6) + a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-11) + a(n-12) - a(n-13).

Empirical g.f.: x*(2 - x - 2*x^4 + x^5 + x^6 - x^7 + 2*x^8 - x^9 - x^10 - x^12) / ((1 - x)*(1 + x)*(1 + x^2)*(1 - 2*x + x^2 - x^4 + x^5 - x^7 + x^8 - x^9)). - Colin Barker, Aug 16 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....1....0....0....1....0....0....1....0....1....1....0
..1....1....0....0....0....0....0....0....0....0....0....0....1....0....0....0
..0....0....0....0....0....0....0....0....0....0....1....1....0....0....1....1
..1....0....0....0....0....0....0....0....0....1....0....0....0....0....0....0
..0....0....0....1....0....0....0....0....1....0....1....0....0....0....1....0
..0....0....0....0....0....0....0....1....0....0....0....0....0....1....0....0
..0....0....1....0....1....0....0....0....0....0....0....0....1....0....0....1

Crossrefs

Cf. A222438.

Sequence in context: A222105 A018059 A291295 * A291297 A347333 A050024

Adjacent sequences: A222428 A222429 A222430 * A222432 A222433 A222434

Keyword

nonn

Author

R. H. Hardin, Feb 20 2013

Status

approved