A269689 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 7+1.

8, 64, 512, 4080, 32416, 256880, 2031072, 16027696, 126262688, 993181680, 7802084704, 61219340720, 479867497248, 3758025752944, 29406845849312, 229946299629360, 1796916741666976, 14034055973604080, 109551619154344032

Offset

1,1

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 43*a(n-2) - 42*a(n-3).

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

G.f.: 8*x*(1 - 6*x - 5*x^2) / ((1 - 7*x)*(1 - 7*x - 6*x^2)).

a(n) = (2^(1-n)*(-73*2^(2+n)*7^n - 7*(7-sqrt(73))^n*(-73+9*sqrt(73)) + 7*(7+sqrt(73))^n*(73+9*sqrt(73)))) / 1533.

(End)

Example

Some solutions for n=5:
..1. .0. .0. .1. .5. .5. .6. .7. .6. .4. .1. .1. .7. .0. .2. .0
..6. .3. .5. .3. .2. .4. .6. .1. .7. .0. .6. .3. .1. .4. .6. .3
..1. .6. .4. .1. .2. .0. .6. .4. .2. .6. .6. .4. .3. .0. .6. .7
..0. .6. .4. .3. .5. .1. .5. .4. .6. .1. .5. .1. .4. .1. .6. .5
..3. .0. .5. .2. .2. .7. .6. .1. .7. .4. .7. .6. .2. .7. .1. .7

Crossrefs

Column 7 of A269690.

Sequence in context: A269618 A269582 A269434 * A269493 A269775 A269655

Adjacent sequences: A269686 A269687 A269688 * A269690 A269691 A269692

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved