A269684 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 2+1.

3, 9, 27, 75, 201, 525, 1347, 3411, 8553, 21285, 52659, 129675, 318153, 778269, 1899267, 4625955, 11249481, 27321525, 66285747, 160679451, 389217513, 942260205, 2280029379, 5514901875, 13334998953, 32235231429, 77906125107

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3).

Conjectures from Colin Barker, Jan 27 2019: (Start)

G.f.: 3*x*(1 - x) / ((1 - 2*x)*(1 - 2*x - x^2)).

a(n) = 3*(-2^(1+n) + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.

(End)

Example

Some solutions for n=9:
..0. .2. .0. .2. .1. .0. .0. .2. .0. .1. .1. .1. .1. .0. .2. .2
..2. .0. .0. .0. .0. .0. .2. .2. .0. .2. .0. .0. .2. .1. .1. .1
..1. .2. .2. .1. .0. .0. .1. .1. .1. .0. .1. .2. .0. .0. .2. .0
..1. .2. .0. .2. .2. .1. .0. .2. .0. .2. .0. .0. .1. .1. .0. .0
..1. .2. .2. .0. .1. .2. .1. .2. .0. .1. .1. .0. .1. .0. .1. .0
..2. .0. .0. .1. .2. .1. .1. .0. .0. .1. .0. .0. .2. .2. .1. .0
..0. .1. .2. .0. .1. .0. .2. .1. .0. .2. .1. .0. .0. .1. .2. .1
..1. .2. .1. .2. .2. .1. .1. .2. .0. .0. .1. .0. .1. .0. .1. .0
..1. .1. .2. .1. .0. .2. .2. .1. .0. .1. .1. .2. .0. .2. .0. .2

Crossrefs

Column 2 of A269690.

Sequence in context: A289658 A180238 A289693 * A330079 A361423 A135415

Adjacent sequences: A269681 A269682 A269683 * A269685 A269686 A269687

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved