A269673 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1.

4, 16, 60, 224, 820, 2976, 10700, 38224, 135780, 480176, 1691740, 5941824, 20814740, 72755776, 253836780, 884207024, 3075861700, 10687549776, 37098781820, 128668433824, 445930140660, 1544500542176, 5346546062860, 18499277662224

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - a(n-2) - 15*a(n-3).

Conjectures from Colin Barker, Jan 26 2019: (Start)

G.f.: 4*x*(1 - x - 4*x^2) / ((1 - 3*x)*(1 - 2*x - 5*x^2)).

a(n) = (-20*3^n + (18-7*sqrt(6))*(1-sqrt(6))^n + (1+sqrt(6))^n*(18+7*sqrt(6))) / 15.

(End)

Example

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

Crossrefs

Column 3 of A269678.

Sequence in context: A269635 A267928 A269532 * A231896 A128650 A072335

Adjacent sequences: A269670 A269671 A269672 * A269674 A269675 A269676

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved