A269675 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 5+1.

6, 36, 210, 1212, 6918, 39156, 220050, 1229292, 6832518, 37810116, 208443090, 1145318172, 6274749318, 34288099476, 186935018130, 1017053643852, 5523244077318, 29944773691236, 162103912681170, 876339613438332

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 13*a(n-2) - 35*a(n-3).

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

G.f.: 6*x*(1 - 3*x - 6*x^2) / ((1 - 5*x)*(1 - 4*x - 7*x^2)).

a(n) = (-924*5^n + (660-195*sqrt(11))*(2-sqrt(11))^n + 15*(2+sqrt(11))^n*(44+13*sqrt(11))) / 385.

(End)

Example

Some solutions for n=6:
..5. .1. .0. .0. .3. .1. .1. .5. .3. .0. .5. .1. .5. .1. .1. .4
..2. .0. .5. .5. .0. .1. .4. .3. .1. .3. .4. .4. .4. .4. .0. .3
..4. .3. .5. .0. .4. .5. .2. .3. .1. .3. .1. .5. .2. .5. .3. .5
..5. .1. .0. .2. .3. .1. .0. .5. .5. .5. .2. .3. .2. .1. .2. .3
..2. .4. .4. .4. .2. .2. .2. .0. .0. .2. .5. .5. .4. .0. .5. .1
..3. .4. .4. .3. .3. .5. .0. .3. .2. .0. .2. .3. .2. .1. .2. .2

Crossrefs

Column 5 of A269678.

Sequence in context: A268941 A269637 A269534 * A269406 A269603 A027910

Adjacent sequences: A269672 A269673 A269674 * A269676 A269677 A269678

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved