A269685 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 3+1.

4, 16, 64, 248, 944, 3544, 13168, 48536, 177776, 647896, 2351728, 8508440, 30701168, 110537560, 397266544, 1425629336, 5109684848, 18295104472, 65449056880, 233970500888, 835908980336, 2984966034520, 10654610339440, 38017445912984

Offset

1,1

Links

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

Formula

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

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

G.f.: 4*x*(1 - 2*x - x^2) / ((1 - 3*x)*(1 - 3*x - 2*x^2)).

a(n) = 2^(-n)*(-17*2^(2+n)*3^n + (51-15*sqrt(17))*(3-sqrt(17))^n + 3*(3+sqrt(17))^n*(17+5*sqrt(17))) / 51.

(End)

Example

Some solutions for n=9:
..1. .0. .1. .2. .0. .2. .0. .1. .0. .0. .1. .0. .0. .0. .1. .0
..2. .3. .3. .0. .3. .0. .3. .0. .1. .3. .1. .1. .0. .1. .0. .2
..0. .1. .0. .3. .2. .1. .0. .2. .2. .0. .1. .2. .2. .3. .0. .3
..0. .2. .0. .0. .1. .0. .2. .2. .3. .2. .2. .3. .2. .2. .3. .1
..0. .1. .1. .1. .3. .1. .2. .0. .1. .2. .3. .2. .2. .1. .1. .3
..2. .1. .2. .3. .0. .0. .1. .2. .1. .1. .1. .1. .0. .2. .3. .3
..0. .3. .1. .2. .2. .0. .3. .1. .0. .2. .3. .0. .0. .0. .0. .0
..0. .1. .0. .1. .3. .3. .1. .3. .1. .2. .2. .1. .2. .1. .0. .1
..3. .3. .0. .2. .3. .1. .0. .0. .2. .1. .1. .3. .2. .2. .2. .3

Crossrefs

Column 3 of A269690.

Sequence in context: A375865 A180239 A006811 * A269614 A267975 A269489

Adjacent sequences: A269682 A269683 A269684 * A269686 A269687 A269688

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved