A269688 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 6+1.

7, 49, 343, 2387, 16541, 114205, 786079, 5396363, 36961757, 252671461, 1724352175, 11750558099, 79971635933, 543661764877, 3692303721631, 25054980870395, 169888502127869, 1151188506903253, 7796069090763247, 52769330311322051

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 31*a(n-2) - 30*a(n-3).

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

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

a(n) = (-7*2^(1+n)*3^n + (21-6*sqrt(14))*(3-sqrt(14))^n + 3*(3+sqrt(14))^n*(7+2*sqrt(14))) / 30.

(End)

Example

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

Crossrefs

Column 6 of A269690.

Sequence in context: A269617 A269581 A269433 * A269492 A269774 A269654

Adjacent sequences: A269685 A269686 A269687 * A269689 A269690 A269691

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved