A221993 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 1,4,6,4,1.

2, 3, 4, 6, 10, 15, 22, 36, 56, 84, 133, 208, 318, 495, 772, 1192, 1846, 2870, 4448, 6886, 10686, 16576, 25679, 39819, 61763, 95732, 148415, 230158, 356829, 553197, 857766, 1329946, 2061917, 3196940, 4956807, 7685148, 11915388, 18474452, 28643620

Offset

1,1

Comments

Column 2 of A221999.

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-3) - 2*a(n-4) - 3*a(n-6) + 2*a(n-7) + a(n-9).

Empirical g.f.: x*(1 + x + x^2)*(2 - x - 3*x^3 + 2*x^4 + x^6) / (1 - x - 3*x^3 + 2*x^4 + 3*x^6 - 2*x^7 - x^9). - 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....1....0....0....1....1....0....1....0....0....0....1
..1....0....0....1....0....0....0....1....0....0....1....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....1....1....0....0
..0....1....0....1....0....0....0....0....1....0....0....0....0....0....0....1
..0....0....1....0....0....0....0....0....0....1....0....0....1....0....0....0
..0....1....0....0....1....0....1....1....0....0....0....0....0....1....0....0
..0....0....0....0....0....0....0....0....0....0....1....1....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: A104977 A206742 A221992 * A221994 A222021 A186426

Adjacent sequences: A221990 A221991 A221992 * A221994 A221995 A221996

Keyword

nonn

Author

R. H. Hardin, Feb 03 2013

Status

approved