A269677 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 7+1.

8, 64, 504, 3936, 30504, 234912, 1799256, 13716480, 104139336, 787814400, 5940850872, 44672407968, 335060917608, 2507328861024, 18723903210264, 139560051510336, 1038430145451144, 7714504288777152, 57228077709064056

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*a(n-1) - 33*a(n-2) - 63*a(n-3).

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

G.f.: 8*x*(1 - 5*x - 8*x^2) / ((1 - 7*x)*(1 - 6*x - 9*x^2)).

a(n) = (-216*7^n + (140-98*sqrt(2))*(3-3*sqrt(2))^n + 14*(3*(1+sqrt(2)))^n*(10+7*sqrt(2))) / 63.

(End)

Example

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

Crossrefs

Column 7 of A269678.

Sequence in context: A268943 A269639 A269536 * A269408 A269605 A269466

Adjacent sequences: A269674 A269675 A269676 * A269678 A269679 A269680

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved